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⚛️ Class XI Physics — Short Questions & Notes
426 real short questions (Section B, including all OR choices) extracted from FBISE Class XI Physics past papers, plus new National Curriculum 2022-23 unit questions, — 1A 2025 (both papers + Old Curriculum), 2A 2025 (+ Old Curriculum), Annual 2023 and Annual 2024 (both papers) — each with a concise model answer (max 3 lines).
📚 How to use: Read each question, attempt it yourself first, then check against the short model answer. These are real Section B short questions exactly as they appeared in the papers — including the OR alternatives, so nothing is skipped.
🗂️ 1A 2025 — Paper I
Q1. Briefly explain 'precision' and 'accuracy' with a diagram.
Ans: Precision means how close repeated measurements are to each other (small least count); accuracy means how close a measurement is to the true value (small fractional error). Dartboard diagram: tight cluster = precise; cluster at centre = accurate.
Q2. How can ordinary light be polarized using polarizers?
Ans: Ordinary light vibrates in all planes. Passing it through a polaroid (polarizer) transmits only vibrations parallel to its transmission axis, producing plane-polarized light; a second polaroid (analyser) confirms it by blocking light when crossed.
Q3. The velocity of a missile travelling at 1500 ms⁻¹ increases to 5000 ms⁻¹ after moving through a distance of 70 km. Calculate the time for the missile to reach this velocity.
Ans: a = (v_f² − v_i²)/2S = (5000² − 1500²)/(2×70000) = 162.5 ms⁻². Then t = (v_f − v_i)/a = 3500/162.5 ≈ 21.5 s.
Q4. A body at 200°C undergoes a reversible isothermal process. The heat energy removed in this process is 7300 J. Calculate the entropy change and discuss entropy sign.
Ans: T = 200 + 273 = 473 K; ΔS = Q/T = −7300/473 ≈ −15.4 J/K. The sign is negative because heat is removed, so the body's entropy (disorder) decreases.
Q5. What is meant by 'conservative' and 'non-conservative' forces? Give one example each.
Ans: A conservative force does work independent of the path (zero work in a closed loop), e.g. gravity. A non-conservative force's work depends on the path taken, e.g. friction.
Q6. What is meant by Magnus effect? Explain with the help of an example.
Ans: A spinning object drags air with it, making air move faster on one side (lower pressure) and slower on the other (higher pressure), so a net force curves its path — e.g. the swing of a spinning cricket ball.
Q7. Differentiate between crystalline and amorphous solids. (Give at least three differences.)
Ans: Crystalline: regular long-range order, sharp melting point, anisotropic (e.g. NaCl, quartz). Amorphous: no long-range order, melt over a range of temperature, isotropic (e.g. glass, plastic).
Q8. Earth completes its one rotation about its axis in 24 hours. Calculate the angular velocity of Earth about its axis in radian per second.
Ans: ω = 2π/T = 2π/(24×3600) = 2π/86400 ≈ 7.27×10⁻⁵ rad s⁻¹.
Q9. The Doppler's effect is used in radar system. Briefly explain the working of radar system.
Ans: A radar transmits radio waves that reflect off a target. The time delay of the echo gives the distance, and the Doppler frequency shift of the reflected wave gives the target's speed (higher frequency = approaching, lower = receding).
Q10. Verify that: (A·B)² + (A×B)² = (AB)²
Ans: (A·B)² + |A×B|² = (ABcosθ)² + (ABsinθ)² = A²B²(cos²θ + sin²θ) = A²B² = (AB)². Verified.
Q11. Calculate KE in electron volt and joules gained by an electron moving through a potential difference of 2 volts.
Ans: KE = qV = e × 2 V = 2 eV; in joules KE = 2 × 1.6×10⁻¹⁹ = 3.2×10⁻¹⁹ J.
Q12. What happens to the density of an object as it moves in a direction with very high speed relative to the speed of light? Justify.
Ans: Density increases: relativistic mass grows as m = m₀/√(1−v²/c²) while length contracts along the motion, so volume decreases. Larger mass ÷ smaller volume = much higher density.
Q13. Why does the resistance of LDR decrease with increase in intensity of light on it?
Ans: An LDR is a semiconductor; incident light photons free extra electron–hole pairs. More light means more charge carriers, so conductivity rises and resistance falls.
Q14. State Faraday's law of electromagnetic induction. Give its mathematical form.
Ans: The induced emf in a circuit is directly proportional to the rate of change of magnetic flux through it: ε = −N(ΔΦ/Δt), the negative sign showing opposition (Lenz's law).
Q15. Does the induced emf in a circuit depend on the resistance of the circuit? Does the induced current depend on the resistance of the circuit? Justify.
Ans: Induced emf depends only on the rate of change of flux (ε = −NΔΦ/Δt), not on resistance. Induced current I = ε/R does depend on resistance — larger R gives smaller current.
Q16. At what speed would the mass of proton be doubled? The rest mass of proton is 1.673×10⁻²⁷ kg.
Ans: m = m₀/√(1−v²/c²) = 2m₀ ⇒ √(1−v²/c²) = ½ ⇒ v² = (3/4)c² ⇒ v = (√3/2)c ≈ 0.866c ≈ 2.6×10⁸ ms⁻¹.
Q17. The kinetic energy of a charged particle moving in a uniform magnetic field does not change. Why? Explain briefly.
Ans: The magnetic force F = qv×B is always perpendicular to the velocity, so it does no work on the particle. It only changes the direction of motion, not the speed, hence KE stays constant.
Q18. If ²³³₉₂U decays twice by alpha particle emission, what is the resulting isotope? Show by equation.
Ans: Each α-decay reduces mass number by 4 and charge number by 2: ²³³₉₂U → ²²⁹₉₀Th + ⁴₂He, then ²²⁹₉₀Th → ²²⁵₈₈Ra + ⁴₂He. The resulting isotope is ²²⁵₈₈Ra (radium-225).
Q19. What is Faraday's cage? Briefly explain its working.
Ans: A Faraday cage is a hollow conducting enclosure. Charges redistribute on its outer surface so the electric field inside remains zero, shielding the interior from external electric fields (e.g. protecting equipment or car passengers in lightning).
Q20. Compare gluons and photons.
Ans: Both are massless force-carrier bosons. The photon mediates the electromagnetic force and carries no charge; the gluon mediates the strong nuclear force, carries colour charge, and remains confined inside hadrons.
Q21. What is meant by annihilation? Give one annihilation reaction.
Ans: Annihilation is when a particle and its antiparticle collide and convert entirely into energy (photons). Example: e⁻ + e⁺ → 2γ (electron–positron annihilation).
Q22. To increase the intensity of wave by a factor of 10, calculate the required increase in amplitude of wave.
Ans: Intensity ∝ (amplitude)², so I′/I = (A′/A)² = 10 ⇒ A′ = √10 A ≈ 3.16 A. Amplitude must be increased about 3.16 times.
Q23. How will the radius of a flexible ring change if it is given negative charge?
Ans: The like (negative) charges distributed on the ring repel one another. The mutual repulsion pushes the ring outward, so its radius increases.
Q24. What is the difference between inertial and non-inertial frame of reference?
Ans: An inertial frame moves with constant velocity (no acceleration) and Newton's laws hold directly. A non-inertial frame is accelerating, so fictitious (pseudo) forces must be introduced to apply Newton's laws.
Q25. Use dimensional analysis to prove the equation P = ρgh is dimensionally homogeneous.
Ans: [P] = ML⁻¹T⁻²; [ρgh] = (ML⁻³)(LT⁻²)(L) = ML⁻¹T⁻². Both sides have the same dimensions, so the equation is dimensionally homogeneous.
Q26. Write three statements of second law of thermodynamics (one in terms of entropy).
Ans: (1) Kelvin: no engine can convert all absorbed heat completely into work. (2) Clausius: heat cannot flow spontaneously from a cold to a hot body. (3) Entropy: the entropy of an isolated system never decreases.
Q27. Derive the relation between torque, moment of inertia and angular acceleration.
Ans: For a particle, F = ma_t = mrα, so torque τ = rF = mr²α. Summing over all particles of a rigid body: τ = (Σmr²)α = Iα.
Q28. What is meant by interference? Give conditions for interference.
Ans: Interference is the superposition of two waves producing reinforcement (constructive) or cancellation (destructive). Conditions: sources must be coherent (constant phase difference), monochromatic (same frequency) and of comparable amplitude.
🗂️ 1A 2025 — Paper II
Q29. Show that the equation P = ρgh is dimensionally homogeneous.
Ans: [P] = ML⁻¹T⁻²; [ρgh] = (ML⁻³)(LT⁻²)(L) = ML⁻¹T⁻². Dimensions of both sides are equal, hence the equation is dimensionally homogeneous.
Q30. Explain that increase in entropy means degradation of energy.
Ans: When entropy increases, ordered useful energy spreads into disordered thermal energy at lower temperature. This energy can no longer be fully converted into work, so it is 'degraded' though not destroyed.
Q31. Time for 10 vibrations of a simple pendulum is 17.6 s. Least count of stop watch is 0.1 s. Find time period of simple pendulum. Also determine uncertainty in it.
Ans: T = 17.6/10 = 1.76 s. Uncertainty = least count/number of vibrations = 0.1/10 = 0.01 s. So T = (1.76 ± 0.01) s.
Q32. When water falls from a tap, its cross-sectional area decreases as it comes down. Explain why?
Ans: By the equation of continuity Av = constant. As water falls it accelerates under gravity, so v increases; therefore the cross-sectional area A must decrease and the stream narrows.
Q33. Under what condition the rectangular (perpendicular) components of a vector have same magnitude?
Ans: When the vector makes 45° with the x-axis: A_x = A cos45° = A_y = A sin45° = A/√2.
Q34. Discuss the motion of two bodies after collision when m₁ << m₂ and v₂ = 0.
Ans: For an elastic collision with m₁ negligible compared to m₂ at rest: v₁′ ≈ −v₁ (the light body bounces back with nearly the same speed) and v₂′ ≈ 0 (the massive body remains practically at rest) — like a ball bouncing off a wall.
Q35. What is meant by Gyroscope? Explain briefly.
Ans: A gyroscope is a rapidly spinning disc mounted so its axis is free to turn. Its large angular momentum keeps the spin axis pointing in a fixed direction (conservation of angular momentum), so it is used in navigation and stabilization.
Q36. What is meant by work? How can work done be calculated graphically by a variable force?
Ans: Work is the dot product of force and displacement, W = Fd cosθ. For a variable force, work done equals the area under the force–displacement graph, found by summing the areas of thin strips.
Q37. A space ship has diameter of 8 m and rotates about its axis to produce artificial gravity of magnitude 17.47 ms⁻² in it. Calculate with which angular speed the satellite rotates?
Ans: r = 8/2 = 4 m; a = ω²r ⇒ ω = √(a/r) = √(17.47/4) ≈ 2.09 rad s⁻¹.
Q38. Differentiate between conservative and non-conservative forces. Give examples.
Ans: Conservative force: work done is path-independent and zero over a closed path (gravity, spring force, electrostatic force). Non-conservative force: work depends on path and energy is dissipated (friction, air resistance).
Q39. Derive the relation between torque, moment of inertia and angular acceleration.
Ans: For each particle F = ma_t = mrα, giving torque τ = rF = mr²α. Adding for the whole rigid body: τ = (Σmr²)α = Iα.
Q40. Derive the formula for kinetic energy [using the equations of motion].
Ans: A body starting from rest under force F gains speed v over distance S: v² = 2aS ⇒ a = v²/2S. Work done W = FS = maS = m(v²/2S)S = ½mv², which equals the KE gained.
Q41. What is meant by Magnus effect? Give its causes and effects.
Ans: Magnus effect is the sideways force on a spinning object moving through air. Cause: spin drags air, making flow faster (lower pressure) on one side and slower (higher pressure) on the other. Effect: the object curves — swing of a spinning ball.
Q42. Differentiate between reversible and irreversible processes. Also give examples.
Ans: Reversible: a quasi-static process that can be retraced without any net change in system or surroundings (very slow isothermal compression). Irreversible: cannot be retraced; entropy increases (friction, free expansion, heat flow hot→cold).
Q43. Show that: Volt/meter = Newton/Coulomb
Ans: V/m = (J/C)/m = (N·m/C)/m = N/C. Hence both are equivalent units of electric field intensity.
Q44. Find the power delivered by an engine for attaining velocity = (4î + 5ĵ) m/s while it exerts a force = (8î − 2ĵ) N.
Ans: P = F·v = (8)(4) + (−2)(5) = 32 − 10 = 22 W.
Q45. What is meant by null method of measurement? Enlist two applications.
Ans: In a null method a circuit is adjusted until the detector reads zero, so the result does not depend on meter calibration — giving high accuracy. Applications: Wheatstone bridge and potentiometer.
Q46. Briefly describe the terms stress, strain and Young's modulus.
Ans: Stress = force per unit area (F/A, unit N m⁻²). Strain = fractional change in length (ΔL/L, dimensionless). Young's modulus Y = stress/strain, a measure of the stiffness of a material.
Q47. Why are the suspension bridges written with their period of use? Why after that period it is dangerous to use the bridge? (Elastic potential)
Ans: Repeated loading–unloading cycles cause fatigue: microscopic permanent (plastic) deformations accumulate in the material. After the stated period the metal may fail even below its elastic limit, so the bridge becomes unsafe.
Q48. What is meant by magnetic flux linkage? Explain briefly.
Ans: Flux linkage is the total magnetic flux linking all N turns of a coil: NΦ. Induced emf equals the rate of change of flux linkage, ε = −Δ(NΦ)/Δt.
Q49. State three statements of second law of thermodynamics (one in terms of entropy).
Ans: (1) Kelvin: no heat engine can convert all absorbed heat into work. (2) Clausius: heat cannot flow by itself from a cold body to a hot body. (3) Entropy: total entropy of an isolated system never decreases.
Q50. How is Doppler's effect helpful in diagnosis of cardiac diseases? Explain briefly.
Ans: In Doppler echocardiography, ultrasound reflected from moving blood cells and heart valves is frequency-shifted. The shift measures blood flow speed and direction, revealing blockages, leaking valves and other cardiac defects.
Q51. Calculate entropy change when 800 g of ice melts at 0°C. Latent heat of fusion for ice is 3.36×10⁵ J/kg. Also discuss sign of entropy.
Ans: Q = mL = 0.8 × 3.36×10⁵ = 2.688×10⁵ J; ΔS = Q/T = 2.688×10⁵/273 ≈ +984 J/K. Positive, because the ice absorbs heat and becomes more disordered (liquid).
Q52. Can sound waves be polarized? Explain briefly.
Ans: No. Polarization is possible only for transverse waves. Sound waves in air are longitudinal — particles vibrate along the direction of propagation — so they cannot be polarized.
Q53. To increase intensity of waves by a factor of 25, calculate the required increase in amplitude of wave.
Ans: I ∝ A² ⇒ A′/A = √25 = 5. The amplitude must be increased 5 times.
Q54. What is super fluidity? Give some of its applications.
Ans: Superfluidity is the frictionless (zero-viscosity) flow of a liquid, shown by liquid helium below 2.17 K — it can even creep up container walls. Applications: cryogenic cooling of magnets/detectors and precision research instruments (e.g. gyroscopes).
Q55. Under what conditions can the terminal potential difference of a battery exceed its emf?
Ans: During charging: current is driven into the battery in reverse, so V = ε + Ir, making terminal potential difference greater than the emf by the drop across internal resistance.
Q56. State the characteristics of vector product.
Ans: A×B is anti-commutative (A×B = −B×A); |A×B| = ABsinθ = area of the parallelogram; direction is perpendicular to both vectors (right-hand rule); A×A = 0; and î×ĵ = k̂ cyclically.
🗂️ 1A 2025 — Old Curriculum 2006
Q57. How many radians account for circumference of a circle? How many steradians account for circumference of a sphere?
Ans: Circle: θ = s/r = 2πr/r = 2π radians. Sphere: Ω = area/r² = 4πr²/r² = 4π steradians.
Q58. What will be the frequency of a simple pendulum if its length is 1 m?
Ans: f = (1/2π)√(g/l) = (1/2π)√(9.8/1) ≈ 3.13/6.28 ≈ 0.5 Hz.
Q59. Show that: |A×B|² + |A·B|² = A²B²
Ans: |A×B|² + (A·B)² = (ABsinθ)² + (ABcosθ)² = A²B²(sin²θ + cos²θ) = A²B². Proved.
Q60. The engine of a JF Thunder fighter develops a thrust of 3000 N. What horse power does it have at a velocity of 600 ms⁻¹?
Ans: P = Fv = 3000 × 600 = 1.8×10⁶ W. In horsepower: 1.8×10⁶/746 ≈ 2413 hp.
Q61. Can the velocity of a body reverse the direction when acceleration is constant? If you think so, give an example.
Ans: Yes. A ball thrown vertically upward moves under constant acceleration g (downward); its velocity decreases, becomes zero at the top, then reverses direction while the acceleration never changes.
Q62. A string 1 m long is used to whirl a 100 g stone in a horizontal circle at a speed of 2 ms⁻¹. Find the tension in the string.
Ans: T = mv²/r = (0.1)(2)²/1 = 0.4 N.
Q63. Calculate the angle of projection for which kinetic energy at summit is equal to one fourth of its kinetic energy at point of projection.
Ans: At the summit only the horizontal component remains: KE_top = ½m(v cosθ)² = KE_i cos²θ. Setting cos²θ = 1/4 ⇒ cosθ = 1/2 ⇒ θ = 60°.
Q64. Show that the relation between maximum height and time of flight of projectile is H = gT²/8.
Ans: H = v²sin²θ/2g and T = 2v sinθ/g ⇒ T² = 4v²sin²θ/g². So gT²/8 = 4v²sin²θ/8g = v²sin²θ/2g = H. Proved.
Q65. A body of mass 2.0 kg is dropped from rest position 5 m above the ground. What is its velocity at height of 3.0 m above the ground?
Ans: Fall distance = 5 − 3 = 2 m; v = √(2gh) = √(2 × 9.8 × 2) = √39.2 ≈ 6.3 ms⁻¹.
Q66. The magnitude of dot and cross product of two vectors are 6√3 and 6 respectively. Find the angle between two vectors.
Ans: tanθ = |A×B|/(A·B) = 6/(6√3) = 1/√3 ⇒ θ = 30°.
Q67. The mass of moon is 1/80 of the mass of earth and the corresponding radius is 1/4 of the earth. Calculate escape velocity at surface of the moon.
Ans: v = √(2GM/R); v_moon = v_earth√((1/80)/(1/4)) = 11.2 × √(1/20) ≈ 11.2 × 0.224 ≈ 2.5 km s⁻¹.
Q68. Is it possible for a person to distinguish between a raw egg and a hard boiled one by spinning each on a table? Explain briefly.
Ans: Yes. The boiled egg spins smoothly like a rigid body. In the raw egg the liquid inside lags behind due to inertia and internal friction, so it wobbles and stops much sooner.
Q69. Determine orbital speed of International Space Station (ISS), if its orbit is 4×10² km above surface of earth.
Ans: v = √(GM/(R+h)) = √(6.67×10⁻¹¹ × 6×10²⁴ / 6.8×10⁶) ≈ √(5.9×10⁷) ≈ 7.7×10³ ms⁻¹ (about 7.7 km/s).
Q70. To what height can a 400 W engine lift a 100 kg mass in 3 s?
Ans: P = mgh/t ⇒ h = Pt/mg = (400 × 3)/(100 × 9.8) = 1200/980 ≈ 1.22 m.
Q71. The moon revolves around the earth in almost a circle of radius 382400 km in 27.3 days. What is the centripetal acceleration?
Ans: ω = 2π/T = 2π/(27.3×86400) ≈ 2.66×10⁻⁶ rad/s; a = ω²r = (2.66×10⁻⁶)² × 3.824×10⁸ ≈ 2.7×10⁻³ ms⁻².
Q72. The deviation of the second order diffracted image formed by an optical grating having 5000 lines per centimeter is 32°. Calculate the wavelength of the light used.
Ans: d = 1/5000 cm = 2×10⁻⁶ m; mλ = d sinθ ⇒ λ = (2×10⁻⁶ × sin32°)/2 = (2×10⁻⁶ × 0.53)/2 ≈ 5.3×10⁻⁷ m = 530 nm.
Q73. Radius of small fog droplet in air is found to be 5.1×10⁻⁶ m. Coefficient of viscosity of air is 1.9×10⁻⁵ kg m⁻¹s⁻¹. Find settling speed of droplet in air.
Ans: v_t = 2ρgr²/9η = (2 × 1000 × 9.8 × (5.1×10⁻⁶)²)/(9 × 1.9×10⁻⁵) ≈ 3.0×10⁻³ ms⁻¹ (about 3 mm/s).
Q74. Modern cars are not rigid but are designed to have "crumple zones" (irregular fold) that collapse upon impact. What is the advantage of this design?
Ans: Crumple zones lengthen the collision time. Since F = Δp/Δt, a longer time means a much smaller force transmitted to the passengers for the same momentum change, reducing injury.
Q75. From the top of a tall building, two tennis balls are dropped, one filled with air and the other with water. Which ball reaches terminal velocity first and why?
Ans: The air-filled (lighter) ball. Terminal velocity is reached when drag equals weight; the lighter ball needs a smaller drag (hence smaller speed) to balance its weight, so it attains terminal velocity first.
Q76. A cricket ball moves past an observer from left to right, spinning counter clockwise. In which direction does the ball tend to deflect?
Ans: By the Magnus effect, the side where spin moves with the airflow has faster flow and lower pressure. For counter-clockwise spin (ball moving left→right) that side is the top, so the ball deflects upward (gains lift).
Q77. A spider swings in the breeze from a silk thread with a period of 0.6 s. How long is the spider's strand of silk?
Ans: T = 2π√(l/g) ⇒ l = gT²/4π² = (9.8 × 0.36)/39.5 ≈ 0.089 m ≈ 8.9 cm.
Q78. If an equation is dimensionally correct, is that equation a right equation?
Ans: Not necessarily. Dimensional correctness is a necessary but not sufficient condition — dimensionless constants (like ½ or 2π) or wrong numerical factors cannot be checked by dimensions.
Q79. The speed of sound in air at 0°C is 332 ms⁻¹. What will be speed of sound at 22°C?
Ans: v_t = v₀ + 0.61t = 332 + 0.61 × 22 ≈ 332 + 13.4 ≈ 345 ms⁻¹.
Q80. Can specific heat of a gas be zero or infinity? Can specific heat be negative?
Ans: Yes: in an adiabatic process C = 0 (Q = 0 though ΔT ≠ 0); in an isothermal process C = ∞ (heat added, ΔT = 0). C can even be negative if the gas is compressed (heated by work) while losing heat, so Q and ΔT have opposite signs.
Q81. X-rays of wavelength 3 nm are incident on a crystal with the lattice spacing is 5 nm. Calculate the angle at which the first Bragg's diffraction is observed.
Ans: 2d sinθ = mλ ⇒ sinθ = λ/2d = 3/(2×5) = 0.3 ⇒ θ ≈ 17.5°.
Q82. Water is flowing smoothly through a closed pipe system. At one point, the speed of water is 3 ms⁻¹, while at another point 3 m higher, the speed is 4 ms⁻¹. At lower point the pressure is 80 kPa. Find the pressure at the upper point.
Ans: Bernoulli: P₂ = P₁ + ½ρ(v₁² − v₂²) − ρgh = 80000 + 500(9 − 16) − 1000×9.8×3 = 80000 − 3500 − 29400 ≈ 47.1 kPa.
Q83. What happens to the temperature of room in which an air conditioner is left running on a table in the middle of a room?
Ans: The room warms up. The AC rejects into the room all the heat it absorbs plus the compressor's work (Q_rejected = Q_absorbed + W), so net heat is added to the room.
Q84. A source of sound vibrates at 200 Hz and is receding from a stationary observer at 18 ms⁻¹. If the speed of sound is 331 ms⁻¹, then what frequency does the observer hear?
Ans: f′ = f·v/(v + u_s) = 200 × 331/(331 + 18) = 66200/349 ≈ 190 Hz.
🗂️ 2A 2025 — New Curriculum
Q85. Derive the relation for centripetal acceleration (a_c) of a body moving in a circle of radius r with velocity v.
Ans: For a small angle, the velocity triangle and position triangle are similar: Δv/v = Δs/r. Dividing by Δt: (Δv/Δt) = (v/r)(Δs/Δt) ⇒ a_c = v²/r, directed toward the centre.
Q86. Find the power delivered by the engine attaining velocity (2,3) m/s, while it exerts a force (7,−3) N.
Ans: P = F·v = (7)(2) + (−3)(3) = 14 − 9 = 5 W.
Q87. What is meant by dot product of two vectors? Give mathematical expression and one example.
Ans: The dot (scalar) product multiplies the magnitude of one vector by the component of the other along it: A·B = ABcosθ. Example: work W = F·d.
Q88. Derive PV = kNT for an ideal gas.
Ans: Kinetic theory gives P = (1/3)(N/V)m⟨v²⟩ ⇒ PV = (2/3)N⟨½mv²⟩. Since average translational KE = (3/2)kT, PV = (2/3)N(3/2)kT = NkT.
Q89. Differentiate between constructive and destructive interference of waves.
Ans: Constructive: crest meets crest, path difference = mλ, amplitudes add (bright fringe/loud sound). Destructive: crest meets trough, path difference = (m + ½)λ, amplitudes cancel (dark fringe/silence).
Q90. A rabbit jumps over an object 0.7 m high: (a) Considering just its vertical motion, calculate its vertical speed when it leaves the ground. (b) How long a time it stays in the air?
Ans: (a) v = √(2gh) = √(2×9.8×0.7) ≈ 3.7 ms⁻¹. (b) t = 2v/g = 2×3.7/9.8 ≈ 0.76 s.
Q91. Briefly describe the terms Stress, Strain, and Young's modulus.
Ans: Stress = deforming force per unit area (F/A). Strain = fractional deformation (ΔL/L). Young's modulus Y = stress/strain — the constant measuring a material's stiffness within the elastic limit.
Q92. Briefly explain the applications of Doppler Effect in radar and astronomy.
Ans: Radar: frequency shift of reflected radio waves gives the speed of planes/cars (speed guns, air-traffic control). Astronomy: red shift of starlight shows galaxies receding (expanding universe), blue shift shows approach.
Q93. What is meant by elastic potential energy? Give its mathematical form.
Ans: Elastic PE is the energy stored in a body when it is elastically deformed (stretched or compressed). For a spring: U = ½kx², where k is spring constant and x the extension.
Q94. A projectile is launched horizontally from the top of a 50 m high cliff and lands at a distance of 20 m from the base of the cliff. Determine the magnitude of the launch velocity.
Ans: Fall time t = √(2h/g) = √(100/9.8) ≈ 3.19 s. Launch velocity v = x/t = 20/3.19 ≈ 6.3 ms⁻¹.
Q95. The energy of photon is given by E = hf, find the dimensions of Planck's constant h, where f is frequency.
Ans: h = E/f ⇒ [h] = ML²T⁻²/T⁻¹ = ML²T⁻¹ (units J·s).
Q96. A point source of sound emits sound energy at a rate of 15 W. Calculate the intensity of sound at a distance of 4 m from the source.
Ans: I = P/4πr² = 15/(4π×16) = 15/201 ≈ 0.075 W m⁻².
Q97. A ball of mass 120 g is released from a height of 30 m. If the ball encounters an air resistance of 0.3 N, find the kinetic energy of the ball just before striking the ground.
Ans: KE = (mg − f)h = (0.12×9.8 − 0.3) × 30 = (1.176 − 0.3) × 30 ≈ 26.3 J.
Q98. Briefly describe the phenomenon of polarization in transverse waves.
Ans: Polarization restricts the vibrations of a transverse wave to a single plane. Unpolarized light vibrating in all planes becomes plane-polarized after passing a polaroid; it proves light waves are transverse.
Q99. Briefly describe the elastic deformation and plastic deformation.
Ans: Elastic deformation: the body regains its original shape when stress is removed (within elastic limit). Plastic deformation: beyond the elastic limit the change becomes permanent and the body stays deformed.
Q100. Calculate the electric field intensity at a distance of 0.5 m from a point charge of 2×10⁻⁶ C in a vacuum.
Ans: E = kq/r² = (9×10⁹ × 2×10⁻⁶)/(0.5)² = 18000/0.25 = 7.2×10⁴ N C⁻¹.
Q101. A current of 2 A is flowing in a copper conductor with a cross-section of 1 mm². Find the drift velocity of the electrons. (For copper, n = 8.5×10²⁸ per m³)
Ans: v_d = I/(nAe) = 2/(8.5×10²⁸ × 10⁻⁶ × 1.6×10⁻¹⁹) ≈ 1.5×10⁻⁴ ms⁻¹.
Q102. Derive the formula for Kinetic Energy [using the equations of motion].
Ans: Starting from rest, v² = 2aS ⇒ a = v²/2S. Work W = FS = maS = ½mv². This work appears as kinetic energy, so KE = ½mv².
Q103. Find the efficiency of a heat engine operating between 427°C and 27°C.
Ans: T₁ = 700 K, T₂ = 300 K; η = 1 − T₂/T₁ = 1 − 300/700 = 0.571 ≈ 57%.
Q104. The electric field at a point due to a point charge is 26 N/C and the electric potential at that point is 13 J/C. Calculate the distance of the point from the charge.
Ans: E = kq/r², V = kq/r ⇒ r = V/E = 13/26 = 0.5 m.
Q105. Determine the relationship for maximum height of a projectile.
Ans: At maximum height v_y = 0: 0 = (v sinθ)² − 2gH ⇒ H = v²sin²θ/2g.
Q106. Differentiate between conservative and non-conservative forces.
Ans: Conservative: work independent of path, zero over a closed loop, PE can be defined (gravity, spring). Non-conservative: work depends on path and dissipates mechanical energy (friction, air drag).
Q107. An object having a net charge of 24 μC is placed in a uniform electric field of 610 N/C directed vertically. What is the mass of this object if it floats in the field?
Ans: Floating ⇒ qE = mg ⇒ m = qE/g = (24×10⁻⁶ × 610)/9.8 ≈ 1.5×10⁻³ kg ≈ 1.5 g.
Q108. A proton is moving in a circular orbit of radius 12 mm in a uniform 0.30 T magnetic field perpendicular to the velocity of the proton. Find the speed of the proton.
Ans: r = mv/qB ⇒ v = qBr/m = (1.6×10⁻¹⁹ × 0.30 × 0.012)/1.67×10⁻²⁷ ≈ 3.4×10⁵ ms⁻¹.
Q109. Find the momentum of a positron moving with relativistic speed. The energy of the positron is 0.47 MeV.
Ans: Using E² = (pc)² + (m₀c²)² with total E = KE + 0.511 = 0.981 MeV: pc = √(0.981² − 0.511²) ≈ 0.84 MeV ⇒ p ≈ 0.84 MeV/c ≈ 4.5×10⁻²² kg·ms⁻¹.
Q110. According to which principle ships float on water? Explain briefly.
Ans: Archimedes' principle: the upthrust equals the weight of fluid displaced. A ship's hollow hull displaces a large volume of water whose weight equals the ship's weight, so it floats.
Q111. Distinguish between crystalline and amorphous solids.
Ans: Crystalline solids have a regular repeating atomic arrangement, sharp melting points and anisotropic properties (NaCl, diamond). Amorphous solids lack long-range order, soften over a temperature range and are isotropic (glass, rubber).
Q112. Calculate the resistance of wire 15 m long that has a diameter of 1.5 mm and resistivity of 2.63×10⁻⁸ Ω·m.
Ans: A = πd²/4 = π(1.5×10⁻³)²/4 ≈ 1.77×10⁻⁶ m²; R = ρL/A = (2.63×10⁻⁸ × 15)/1.77×10⁻⁶ ≈ 0.22 Ω.
🗂️ 2A 2025 — Old Curriculum 2006
Q113. Briefly explain the difference between systematic errors (including zero error) and random errors with suitable examples.
Ans: Systematic errors shift all readings in one direction due to a faulty instrument or technique (e.g. a screw gauge's zero error); corrected by calibration. Random errors scatter readings unpredictably in both directions (e.g. reaction-time errors); reduced by averaging repeated readings.
Q114. State Newton's Third Law of Motion. How it leads to the law of conservation of momentum? Give one example.
Ans: To every action there is an equal and opposite reaction. In a collision F₁₂ = −F₂₁ act for equal times, so impulses are equal and opposite and total momentum stays constant. Example: recoil of a gun when a bullet is fired.
Q115. Describe the head-to-tail rule for vector addition with a simple diagram.
Ans: Draw the first vector, place the tail of the second at the head of the first (and so on). The resultant is the vector drawn from the tail of the first to the head of the last.
Q116. Give any three drawbacks of conventional sources of energy.
Ans: (1) Fossil fuels are finite and depleting fast. (2) Burning them causes air pollution and greenhouse gases (global warming). (3) Their extraction/prices are costly and environmentally damaging.
Q117. Draw and interpret a velocity–time graph of an object moving with uniform acceleration. How can the slope of this graph be used to find acceleration?
Ans: For uniform acceleration the v–t graph is a straight line rising with time. Slope = Δv/Δt = acceleration; the steeper the line, the greater the acceleration (area under it gives distance).
Q118. A garden hose of inner radius 1.1 cm carries water at 2.50 m/s; the nozzle at the end has radius 0.25 cm. How fast does the water emerge out through the nozzle?
Ans: A₁v₁ = A₂v₂ ⇒ v₂ = v₁(r₁/r₂)² = 2.50 × (1.1/0.25)² = 2.50 × 19.36 ≈ 48.4 ms⁻¹.
Q119. How force is equal to the rate of change of momentum? Show mathematically.
Ans: F = ma = m(v_f − v_i)/t = (mv_f − mv_i)/t = Δp/Δt. Hence force equals the rate of change of momentum (Newton's second law).
Q120. Briefly describe: a. Radian b. Steradian
Ans: Radian: plane angle subtended at the centre of a circle by an arc equal in length to the radius. Steradian: solid angle subtended at the centre of a sphere by a surface area equal to r².
Q121. What is meant by work in Physics? Under what conditions work becomes positive and negative?
Ans: Work W = Fd cosθ, the dot product of force and displacement. Positive when 0° ≤ θ < 90° (force helps motion); negative when 90° < θ ≤ 180° (force opposes motion, e.g. friction); zero at θ = 90°.
Q122. Briefly explain the first and second conditions of equilibrium.
Ans: First condition: the vector sum of all forces is zero (ΣF = 0) — no translational acceleration. Second condition: the sum of all torques about any axis is zero (Στ = 0) — no rotational acceleration.
Q123. Show that the work done by gravity on a body depends only on the initial and final positions, not on the path followed.
Ans: Split any path into small horizontal and vertical steps: gravity does no work on horizontal parts (F⊥d) and mgΔh on vertical parts. Total W = mg(h₁ − h₂) — depends only on the height difference, proving gravity is conservative.
Q124. The deviation of the second order diffracted image formed by an optical grating having 4000 lines per centimeter is 32°. Calculate the wavelength of light used.
Ans: d = 1/4000 cm = 2.5×10⁻⁶ m; λ = d sinθ/m = (2.5×10⁻⁶ × 0.53)/2 ≈ 6.6×10⁻⁷ m ≈ 662 nm.
Q125. Derive the expression for centripetal acceleration a_c = v²/r.
Ans: For a small displacement on the circle, the velocity and radius triangles are similar: Δv/v = Δs/r. Dividing by Δt gives a = (v/r)(Δs/Δt) = v²/r, directed toward the centre.
Q126. Briefly explain that increase in entropy means degradation of energy.
Ans: As entropy rises, useful ordered energy disperses into random molecular motion at lower temperature. That energy can no longer be fully recovered as work — it is degraded, though conserved in amount.
Q127. What is orbital velocity? Derive the mathematical form for orbital velocity.
Ans: Orbital velocity is the speed needed for a satellite to stay in circular orbit. Gravity supplies centripetal force: GMm/r² = mv²/r ⇒ v = √(GM/r) (≈ √(gR) near Earth's surface).
Q128. Briefly describe the terms amplitude, period and frequency.
Ans: Amplitude: maximum displacement from the mean position. Period T: time for one complete vibration. Frequency f: number of vibrations per second; f = 1/T (unit Hz).
Q129. Derive the relation to determine the maximum range of projectile.
Ans: R = v_x × T = v cosθ × (2v sinθ/g) = v² sin2θ/g. R is maximum when sin2θ = 1, i.e. θ = 45°, giving R_max = v²/g.
Q130. How a viscous fluid undergoes transition from laminar flow to turbulent flow when velocity increases? Explain briefly.
Ans: At low speeds fluid layers slide smoothly (laminar). Above a critical velocity, inertial forces dominate viscous forces; streamlines break up into irregular eddies and the flow becomes turbulent.
Q131. Water is flowing smoothly through a pipe. At one point the pressure is 33.2 kPa and the speed of water 2 m/s. While at another point 2.3 m higher the pressure is 3.7 kPa, at what speed is the water flowing through this point?
Ans: Bernoulli: ½ρv₂² = (P₁ − P₂) + ½ρv₁² − ρgh = 29500 + 2000 − 22540 = 8960 ⇒ v₂² = 17.9 ⇒ v₂ ≈ 4.2 ms⁻¹.
Q132. A reversible engine works between two temperatures whose difference is 70°C. If it absorbs 770 J of heat from the source and rejects 570 J to the sink, calculate the temperature of the source and the sink.
Ans: η = W/Q₁ = 200/770 = ΔT/T₁ = 70/T₁ ⇒ T₁ = 770×70/200 = 269.5 K (source); T₂ = 269.5 − 70 = 199.5 K (sink).
Q133. State the necessary conditions for the execution of Simple Harmonic Motion (SHM).
Ans: (1) A restoring force proportional to displacement and directed toward the mean position (F = −kx). (2) The system must possess inertia and elasticity. (3) Frictional losses should be negligible.
Q134. Briefly explain the phenomenon of weightlessness experienced by astronauts in orbit.
Ans: The spacecraft and astronaut are both in continuous free fall toward Earth — gravity acts purely as centripetal force. With no supporting (normal) force between astronaut and craft, apparent weight is zero.
Q135. How can a pressure difference arise due to different rates of fluid flow? Explain according to Bernoulli effect.
Ans: By Bernoulli's principle, where fluid speed is high the pressure is low and vice versa (P + ½ρv² = constant). Thus different flow speeds at two points create a pressure difference — the basis of lift on wings and atomizers.
Q136. In a ripple tank 50 waves passes through a certain point in one second. If the wavelength of the waves is 4 cm, then find the speed of the waves.
Ans: f = 50 Hz, λ = 0.04 m ⇒ v = fλ = 50 × 0.04 = 2 ms⁻¹.
Q137. What is the change in entropy of 50 g of water at 273 K as it is changed into ice at 273 K? Take the latent heat of fusion of ice = 336000 J kg⁻¹.
Ans: Q = mL = 0.05 × 336000 = 16800 J (removed); ΔS = −Q/T = −16800/273 ≈ −61.5 J/K. Negative because water loses heat and becomes more ordered (ice).
Q138. What is meant by gravitational potential energy? How it can be positive or negative depending on the choice of reference level?
Ans: Gravitational PE is the energy a body has due to its position in a gravitational field, U = mgh. Since h is measured from an arbitrary reference level, U is positive above that level and negative below it.
Q139. 25200 J of heat is supplied to the system while the system does 6000 J of work. Calculate the change in internal energy of the system.
Ans: First law: ΔU = Q − W = 25200 − 6000 = 19200 J.
Q140. How the horizontal component of the normal force provides the required centripetal acceleration?
Ans: On a banked road the normal force tilts with the surface. Its vertical component balances weight (N cosθ = mg) while its horizontal component points to the centre: N sinθ = mv²/r, giving tanθ = v²/rg.
🗂️ Annual 2023
Q141. Differentiate between random and systematic errors.
Ans: Random errors fluctuate unpredictably in both directions (e.g. human timing errors) and are reduced by averaging. Systematic errors bias every reading the same way due to faulty apparatus or zero error and are removed by calibration.
Q142. Check if the famous Einstein equation E = mc² is dimensionally consistent.
Ans: [mc²] = M(LT⁻¹)² = ML²T⁻² = dimensions of energy [E]. Both sides match, so the equation is dimensionally consistent.
Q143. Two coplanar vectors A and B are making an angle of 60° with respect to each other having magnitudes of 4 unit and 5 unit respectively. Find area of parallelogram formed by these vectors.
Ans: Area = |A×B| = ABsinθ = 4 × 5 × sin60° = 20 × 0.866 ≈ 17.3 square units.
Q144. The velocity time graph shows the motion of bicyclist: (a) From the slope of the graph calculate the acceleration of the bicyclist between A and B, B and C, C and D & D and E. (b) Calculate the average acceleration of the bicyclist.
Ans: Acceleration of each part = slope = Δv/Δt of that segment (e.g. A–B rising ⇒ positive a; B–C horizontal ⇒ a = 0; D–E falling ⇒ negative a). Average acceleration = (v_final − v_initial)/total time taken over the whole journey.
Q145. Under what condition the sum of three vectors results into a null vector? Briefly explain with diagram.
Ans: When the three vectors, taken head-to-tail, form a closed triangle — i.e. the resultant of any two is equal and opposite to the third. Then A + B + C = 0.
Q146. Describe the term 'escape velocity'. Write its formula in terms of G, m and R.
Ans: Escape velocity is the minimum speed with which a body must be projected to escape a planet's gravity permanently: v_esc = √(2Gm/R) ≈ 11.2 km/s for Earth.
Q147. Show that work done on a body is equal to change in its Kinetic energy.
Ans: W = FS = maS. Using v_f² − v_i² = 2aS: W = m(v_f² − v_i²)/2 = ½mv_f² − ½mv_i² = ΔKE (work–energy principle).
Q148. What is power? Show power as product of force and velocity.
Ans: Power is the rate of doing work: P = W/t = F·d/t = F·v. Unit: watt (W).
Q149. Does the apparent weight of a body inside a lift become double, if lift is accelerating upward with acceleration equal to gravitational acceleration (g)? Justify your answer.
Ans: Yes. Apparent weight N = m(g + a); with a = g, N = 2mg — exactly double the true weight.
Q150. What is banking of road? Show that angle of banking is correct for one speed.
Ans: Banking is tilting the road at bends so the horizontal component of normal force supplies centripetal force: N sinθ = mv²/r, N cosθ = mg ⇒ tanθ = v²/rg. A fixed θ satisfies this for only one speed v = √(rg tanθ).
Q151. Why does a diver changes his/her body position before and after diving in the pool?
Ans: Angular momentum L = Iω is conserved. Tucking in limbs reduces moment of inertia I, so ω increases and the diver spins faster; stretching out before entry increases I and slows the spin for a clean entry.
Q152. Discuss aerofoil. State one practical example of aerofoil briefly.
Ans: An aerofoil is a curved surface shaped so air moves faster over the top than the bottom; by Bernoulli's principle the pressure above is lower, producing lift. Example: an airplane wing.
Q153. What is meant by moment of inertia? Write its mathematical expression and SI units.
Ans: Moment of inertia is the rotational analogue of mass — a body's resistance to change in rotational motion: I = Σmr². SI unit: kg·m².
Q154. What is resonance phenomenon? Give one example in which resonance plays an important role.
Ans: Resonance is the large-amplitude vibration produced when the driving frequency equals the natural frequency of a system. Example: tuning a radio — the circuit resonates with the selected station's frequency (also microwave-oven heating).
Q155. The speed of a wave on a particular string is 32 m/s. If the string is 8 m long, to what frequency will it resonate?
Ans: Fundamental mode: λ = 2L = 16 m ⇒ f = v/λ = 32/16 = 2 Hz.
Q156. The magnitude of the viscous force in fluid flow depends on the shape and velocity of the object. Justify.
Ans: Stokes' law F = 6πηrv shows drag grows with size/geometry (r, shape factor) and speed v — a larger or faster object displaces more fluid layers per second, so friction between layers increases.
Q157. What is the effect of variation of pressure on the speed of sound in gas?
Ans: No effect. v = √(γP/ρ); at constant temperature increasing P increases ρ in the same ratio, so P/ρ — and hence the speed of sound — remains unchanged.
Q158. Briefly explain the function of compensator plate in Michelson interferometer.
Ans: One beam passes through the beam-splitter glass three times, the other only once. The compensator plate (same glass, same thickness) is placed in the second beam to equalize the optical paths for all wavelengths.
Q159. Is it useful to leave an air-conditioner left running on a table in the middle of the room? What will happen to the temperature of the room?
Ans: Not useful. The unit rejects into the same room all the heat it absorbs plus the compressor's work, so the room's temperature actually rises instead of falling.
Q160. Give two statements for the second law of thermodynamics.
Ans: Kelvin: it is impossible to build an engine that converts all the heat it absorbs completely into work. Clausius: heat cannot flow spontaneously from a colder body to a hotter body.
🗂️ Annual 2024 — Paper I
Q161. Under what conditions two or more sources of light behave as coherent sources?
Ans: When they emit waves of the same frequency (monochromatic) with a constant phase difference. Practically this is achieved by deriving both beams from a single source, as in Young's double slit.
Q162. Why flash of lightning is seen earlier than the thunder? Explain briefly.
Ans: Light travels at 3×10⁸ ms⁻¹ while sound travels at only about 340 ms⁻¹. The flash reaches us almost instantly, whereas the thunder takes roughly 3 s per kilometre, so it is heard later.
Q163. Differentiate between precision and accuracy.
Ans: Precision is how close repeated measurements are to one another — determined by the instrument's least count. Accuracy is how close a measurement is to the true value — determined by the fractional error.
Q164. Show that: |A×B|² + |A·B|² = A²B²
Ans: (ABsinθ)² + (ABcosθ)² = A²B²(sin²θ + cos²θ) = A²B². Proved.
Q165. Under what circumstances would a vector has components that are equal in magnitude? Explain graphically.
Ans: When the vector bisects the angle between the axes, i.e. makes 45° with the x-axis: A_x = Acos45° = A_y = Asin45° = A/√2. Graphically the vector lies along the diagonal of a square.
Q166. Describe the limitations of dimensional analysis.
Ans: It cannot determine dimensionless constants (½, 2π); it cannot handle trigonometric, exponential or logarithmic functions; and it cannot derive relations involving sums of terms or more variables than the base dimensions allow.
Q167. For a projectile show that: R = R_max Sin2θ
Ans: R = v²sin2θ/g. Range is maximum at θ = 45°: R_max = v²/g. Substituting v²/g = R_max gives R = R_max sin2θ.
Q168. Differentiate between conservative and non-conservative forces.
Ans: Conservative: work is path-independent and zero round a closed path; mechanical energy is conserved (gravity, spring force). Non-conservative: work depends on the path and dissipates energy as heat (friction, air resistance).
Q169. Show that the given equation is dimensionally consistent: 2as = v_f² − v_i²
Ans: [2as] = (LT⁻²)(L) = L²T⁻²; [v²] = (LT⁻¹)² = L²T⁻². Both sides have identical dimensions, so the equation is dimensionally consistent.
Q170. A machine needs 500 J of energy to raise 5 kg block at distance of 3.0 m. Find the efficiency of machine.
Ans: Useful output = mgh = 5 × 9.8 × 3 = 147 J. Efficiency = output/input × 100 = 147/500 × 100 ≈ 29.4%.
Q171. Differentiate between radian and steradians. Show that number of steradians in sphere are equal to 4π Sr.
Ans: Radian measures plane angle (arc/radius); steradian measures solid angle (area/r²). For a full sphere: Ω = 4πr²/r² = 4π steradians.
Q172. Describe angular displacement, and angular acceleration. Express angular displacement in radian.
Ans: Angular displacement is the angle swept by the radius: θ = s/r (radian). Angular acceleration is the rate of change of angular velocity: α = Δω/Δt (rad s⁻²).
Q173. Briefly explain the equation tanθ = v²/rg, relating banking angle 'θ' to speed 'v' and radius of curvature 'r'.
Ans: On a banked curve, N cosθ = mg and N sinθ = mv²/r. Dividing: tanθ = v²/rg — the ideal banking angle grows with speed and decreases with a larger radius, letting the car turn without relying on friction.
Q174. Why fog droplets appear to be suspended in air? Explain briefly.
Ans: Terminal velocity ∝ r² (Stokes' law). Fog droplets are so tiny that their terminal velocity is only millimetres per second — they fall imperceptibly slowly and so appear suspended.
Q175. What is the moment of inertia of a 50 kg sphere whose radius is 25 cm?
Ans: I = (2/5)MR² = 0.4 × 50 × (0.25)² = 0.4 × 50 × 0.0625 = 1.25 kg·m².
Q176. A certain pipe has a cross-sectional area of 0.0002 m² in which water is flowing at 5 m/s. Find flow rate.
Ans: Flow rate = Av = 0.0002 × 5 = 0.001 m³ s⁻¹ (= 1 litre per second).
Q177. Why is there weightlessness in artificial satellite? Explain briefly.
Ans: The satellite and everything in it fall freely toward Earth with the same acceleration — gravity acts entirely as centripetal force. With no reaction (normal) force on the occupants, their apparent weight is zero.
Q178. In a ripple tank 20 waves passes through a certain point in one second. If the wave length of wave is 4 cm then find the speed of wave.
Ans: f = 20 Hz, λ = 0.04 m ⇒ v = fλ = 20 × 0.04 = 0.8 ms⁻¹.
Q179. How the amplitude of a forced oscillation changes with frequency near to the natural frequency of the systems? Describe graphically.
Ans: As the driving frequency approaches the natural frequency, amplitude rises sharply and peaks at resonance, then falls off beyond it. The resonance curve is taller and narrower for light damping, lower and broader for heavy damping.
Q180. How the variation of pressure affects speed of sound in air? Explain briefly.
Ans: It has no effect: v = √(γP/ρ). At constant temperature, raising the pressure raises the density proportionally, so the ratio P/ρ — and hence v — stays constant.
Q181. Briefly explain Brewster's law of polarization.
Ans: When light strikes a transparent medium at the polarizing angle θ_p, the reflected ray is completely plane-polarized and is perpendicular to the refracted ray. Brewster's law: tanθ_p = n (refractive index).
Q182. Calculate work done by a thermodynamic system during volume change.
Ans: For expansion at pressure P through volume change ΔV, work done by the system W = PΔV — equal to the area under the P–V curve.
Q183. Why do the systems tend to become less orderly over time? Explain briefly.
Ans: Disordered arrangements are overwhelmingly more probable than ordered ones. Natural processes therefore move toward states of higher probability — higher entropy — in accordance with the second law of thermodynamics.
Q184. Briefly explain diffraction of X-rays through crystals.
Ans: X-ray wavelengths are comparable to atomic spacings, so regularly spaced crystal planes act as a 3-D diffraction grating. Reflected beams reinforce when Bragg's condition 2d sinθ = mλ is met, revealing crystal structure.
Q185. How are colour patterns formed in interference of light through thin films? Explain briefly.
Ans: Light reflected from the top and bottom surfaces of the film interferes. The path difference depends on film thickness and viewing angle, so different wavelengths reinforce at different places, producing coloured fringes (soap bubbles, oil films).
Q186. Determine the two complementary angles at which the horizontal ranges of two projectiles become equal when velocity of projections and the acceleration due to gravity are kept constant.
Ans: R = v²sin2θ/g and sin2(90° − θ) = sin(180° − 2θ) = sin2θ, so complementary angles θ and (90° − θ) give equal ranges — e.g. 30° and 60°.
Q187. Briefly explain adiabatic process by using first law of thermodynamics.
Ans: In an adiabatic process no heat enters or leaves (Q = 0), so the first law gives ΔU = −W: work done by the gas comes from internal energy (cooling on expansion), and work done on the gas raises it (heating on compression).
Q188. What is meant by impulse? How it can be related to momentum of body? Explain briefly.
Ans: Impulse is the product of force and the time for which it acts: J = FΔt. Since F = Δp/Δt, impulse equals the change in momentum: J = Δp = mv_f − mv_i.
🗂️ Annual 2024 — Paper II
Q189. Briefly explain the main principle behind the use of ultrasound to obtain diagnostic information about internal structure.
Ans: High-frequency sound pulses partially reflect at boundaries between tissues of different densities. Measuring the timing and strength of the returning echoes lets a scanner map internal organs (echo-location principle).
Q190. Why does a cricket player retract his hand while catching the ball? (Describe in context of impulse)
Ans: Retracting the hand increases the stopping time Δt. Since F = Δp/Δt and the momentum change is fixed, a longer time means a smaller force on the hands, preventing injury.
Q191. If (A+B) and (A−B) are perpendicular to each other, then show that A and B are of the same magnitude.
Ans: Perpendicular ⇒ (A+B)·(A−B) = 0 ⇒ A·A − B·B = A² − B² = 0 ⇒ A = B. Proved.
Q192. Two wave pulses travelling in opposite direction completely cancel each other. What happens to energy possessed by waves? Briefly explain.
Ans: The energy is not destroyed. At the instant of cancellation the displacement is zero but the medium's particles carry all the energy as kinetic energy; the pulses then re-emerge unchanged and carry it onward.
Q193. How artificial gravity is created to counter balance weightlessness? Describe briefly.
Ans: The spacecraft is rotated about its axis. Occupants at the rim need a centripetal force, supplied by the floor pushing on them; this normal force feels like gravity of magnitude a = ω²r, so spin rate sets the desired 'g'.
Q194. Show that following equations are homogeneous with respect to dimensions: (i) a_c = v²/r (ii) E = mc²
Ans: (i) [v²/r] = (LT⁻¹)²/L = LT⁻² = [a]. (ii) [mc²] = M(LT⁻¹)² = ML²T⁻² = [E]. Both equations are dimensionally homogeneous.
Q195. Why kinetic energy of system does not remain constant in inelastic collision? Explain briefly.
Ans: In an inelastic collision part of the kinetic energy is converted into heat, sound and permanent deformation of the bodies. Momentum is still conserved, but KE after collision is less than before.
Q196. Show that S = v_i t + ½at² is dimensionally consistent.
Ans: [v_i t] = (LT⁻¹)(T) = L; [½at²] = (LT⁻²)(T²) = L; [S] = L. All terms have the dimension of length, so the equation is dimensionally consistent.
Q197. Differentiate between radian and steradian. Show that number of steradians in sphere are equal to 4π Sr.
Ans: Radian: plane angle = arc/radius. Steradian: solid angle = surface area/r². Whole sphere: Ω = 4πr²/r² = 4π steradians.
Q198. State the conditions of equilibrium with mathematical expressions.
Ans: First condition: ΣF = 0 (ΣF_x = 0, ΣF_y = 0) — no linear acceleration. Second condition: Στ = 0 about any axis — no angular acceleration.
Q199. Show that the angles of projection, that exceed or fall short of 45° by equal amount, ranges are equal.
Ans: For θ = 45° ± α: 2θ = 90° ± 2α and sin(90° + 2α) = sin(90° − 2α) = cos2α. Since R = v²sin2θ/g, both angles give the same range.
Q200. Work done can be calculated from the area under force-displacement graph. Illustrate your answer.
Ans: Divide the F–d curve into thin strips; each strip's area FΔd is the small work done over Δd. Summing all strips, total work = total area under the graph — valid even for a variable force.
Q201. Differentiate between renewable and non-renewable energy sources.
Ans: Renewable sources are naturally replenished and non-polluting — solar, wind, hydro, tidal, geothermal. Non-renewable sources are finite and exhaustible — coal, oil, natural gas (fossil fuels) and uranium.
Q202. What is meant by moment of inertia of body and angular momentum?
Ans: Moment of inertia I = Σmr² is a body's resistance to change in its rotational motion. Angular momentum L = Iω (= r×p for a particle) is the rotational analogue of linear momentum.
Q203. Differentiate between absolute uncertainty and percentage uncertainty with examples.
Ans: Absolute uncertainty is the doubt expressed in the same units as the measurement, e.g. (5.0 ± 0.1) cm. Percentage uncertainty = (absolute/measured value) × 100, e.g. 0.1/5.0 × 100 = 2%.
Q204. Is there any work done by centripetal force? Elaborate your answer.
Ans: No. Centripetal force is always perpendicular to the displacement (which is along the tangent), so W = Fd cos90° = 0. It changes direction of motion, never the speed.
Q205. An electric motor turns at 200 rpm. What is the angular velocity? What is angular displacement after 5 sec?
Ans: ω = 2πf = 2π × 200/60 ≈ 20.9 rad s⁻¹; θ = ωt = 20.9 × 5 ≈ 104.7 rad.
Q206. Why clouds appear to float in air? Explain briefly.
Ans: Cloud droplets are extremely small, so their terminal velocity (∝ r² by Stokes' law) is negligibly small. Rising air currents easily balance this slow fall, so clouds appear to float.
Q207. A small circular hole 4.00 mm in diameter is cut in the side of a large water tank, 12 m below the water level in the tank. The top of tank is open to the air. Find speed of efflux of water and the volume discharged per second.
Ans: v = √(2gh) = √(2×9.8×12) ≈ 15.3 ms⁻¹; A = πr² = π(2×10⁻³)² ≈ 1.26×10⁻⁵ m²; Q = Av ≈ 1.9×10⁻⁴ m³ s⁻¹.
Q208. Briefly explain any two applications of resonance.
Ans: (1) Radio/TV tuning: the receiving circuit is adjusted to resonate with the desired station's frequency. (2) Microwave oven: microwaves at the resonant frequency of water molecules make them vibrate vigorously, heating food.
Q209. How ultrasonic waves can be detected by using piezoelectric method? Briefly explain.
Ans: When ultrasonic pressure waves strike a piezoelectric crystal (e.g. quartz), the alternating mechanical stress produces an alternating voltage across its faces of the same frequency — this electrical signal is amplified and detected.
Q210. Discuss necessary conditions for detectable interference of light.
Ans: Sources must be coherent (constant phase difference) and monochromatic (same wavelength); amplitudes should be comparable; and the sources/slits must be narrow and close together so fringes are wide enough to observe.
Q211. Explain briefly the function of moveable plane mirror used in Michelson's interferometer.
Ans: Moving the mirror changes the path length of one beam. Each λ/2 displacement shifts the pattern by one fringe, so counting fringes (m) measures distance precisely: d = mλ/2.
Q212. How is energy degraded in all natural processes? Explain briefly.
Ans: In every natural (irreversible) process some useful energy changes into random heat at lower temperature — friction, resistance, etc. This energy cannot be fully reconverted into work, so the quality of energy continually degrades while entropy rises.
Q213. Why molar specific heat at constant pressure is greater than molar specific heat at constant volume? Give reason.
Ans: At constant volume all heat raises internal energy. At constant pressure the gas also expands and does external work, so extra heat is needed for the same temperature rise: C_p = C_v + R, hence C_p > C_v.
Q214. When Young's double slit experiment apparatus is taken from air into water, what will happen to the interference pattern?
Ans: In water the wavelength decreases (λ′ = λ/n). Since fringe width Y = λL/d, the fringes come closer together — the pattern shrinks but remains visible.
Q215. Write two statements of second law of thermodynamics.
Ans: Kelvin: no process can convert all absorbed heat completely into work. Clausius: heat cannot flow of itself from a cold body to a hot body without external work.
Q216. How can the fringe width be increased in Young's double slit experiment? Briefly explain.
Ans: Fringe width Y = λL/d. It can be increased by using light of longer wavelength, increasing the slit-to-screen distance L, or decreasing the separation d between the slits.
📘 New: National Curriculum 2022-23 Chapters (Q217-426)
📚 Note: The 210 questions below are organized by the 14 units (Unit 1-14) of the official Model Textbook of Physics Class XI, National Curriculum 2022-23 — Physical Quantities & Measurements, Vectors, Translatory Motion, Rotational & Circular Motion, Work & Kinetic Energy, Fluid Mechanics, Physics of Solids, Heat & Thermodynamics, Waves, Electrostatics, Electricity, Magnetism, Relativity, and Particle Physics.
🗂️ Unit 1: Physical Quantities and Measurements
Q217. What is the difference between a base quantity and a derived quantity?
Ans: A base quantity is one of the seven fundamental quantities (like mass, length, time) defined independently, while a derived quantity is expressed in terms of base quantities using a defining equation (e.g., velocity = displacement/time).
Q218. Define an 'estimation' in physics.
Ans: An estimation is a rough educated guess of the value of a physical quantity, made using prior experience and sound physical reasoning, rather than an exact measurement.
Q219. Distinguish between accuracy and precision in measurement.
Ans: Accuracy refers to how close a measured value is to the true or accepted value, while precision refers to how consistently repeated measurements agree with one another, regardless of whether they are close to the true value.
Q220. What is the least count of a measuring instrument?
Ans: The least count is the smallest value that an instrument can measure or the smallest division it can read directly, such as 0.01 mm for a typical screw gauge.
Q221. Explain the difference between random error and systematic error.
Ans: Random errors are unpredictable fluctuations that can be reduced by taking multiple readings and averaging, while systematic errors are consistent, repeatable errors (often due to faulty calibration) that shift all readings in the same direction.
Q222. Why is dimensional analysis useful, and what is one of its limitations?
Ans: Dimensional analysis is useful for checking whether an equation is homogeneous (dimensionally consistent) and for deriving relationships between quantities; its main limitation is that it cannot determine dimensionless numerical constants in a formula.
Q223. Give an example of how estimation can be used in everyday life.
Ans: Estimating the height of a building by counting its floors and estimating the height of a single floor, then multiplying, is a common everyday application of estimation.
Q224. What is meant by 'significant figures' in a measurement?
Ans: Significant figures are the digits in a measured value that carry meaningful information about its precision, including all certain digits plus one estimated digit.
Q225. Why is it important to take multiple readings when performing an experiment?
Ans: Taking multiple readings and averaging them helps minimize the effect of random errors, producing a more reliable and precise result.
Q226. State the SI base quantities and their units for mass, length, and time.
Ans: Mass is measured in kilograms (kg), length in metres (m), and time in seconds (s), all recognized as SI base quantities.
Q227. How can the mass of an irregularly shaped object be estimated using density and volume?
Ans: By first estimating the object's volume (using an appropriate geometric model) and then multiplying by an estimated average density, since mass = density × volume.
Q228. What does it mean for an equation to be 'dimensionally correct'?
Ans: An equation is dimensionally correct if the dimensions of the quantities on both sides of the equation are identical, confirming consistency, though this does not guarantee the equation is numerically correct.
Q229. Why might a vernier callipers be preferred over a standard ruler for certain measurements?
Ans: A vernier callipers has a much smaller least count than a standard ruler, allowing for more precise measurements of small lengths, diameters, or thicknesses.
Q230. What is a zero error, and how does it affect measurements?
Ans: A zero error occurs when an instrument does not read exactly zero when it should, causing a constant systematic offset in all subsequent measurements unless corrected.
Q231. Explain briefly why estimating physical quantities is considered a valuable skill in science and engineering.
Ans: Estimation develops a physical sense and intuition for the scale of quantities, allowing scientists and engineers to quickly judge whether a calculated or measured result is reasonable, even without exact data.
🗂️ Unit 2: Vectors
Q232. What is the difference between a scalar and a vector quantity? Give one example of each.
Ans: A scalar quantity has only magnitude (e.g., mass), while a vector quantity has both magnitude and direction (e.g., displacement).
Q233. State the triangle law of vector addition.
Ans: If two vectors are represented in magnitude and direction by two sides of a triangle taken in order, their resultant is represented by the third side of the triangle, taken in the opposite order.
Q234. Define the dot (scalar) product of two vectors and state its formula.
Ans: The dot product of two vectors A and B is a scalar quantity given by A·B = AB cosθ, where θ is the angle between them.
Q235. Define the cross (vector) product of two vectors and state its formula.
Ans: The cross product of two vectors A and B is a vector quantity with magnitude AB sinθ, directed perpendicular to the plane containing A and B, determined by the right-hand rule.
Q236. How is torque related to the cross product of vectors?
Ans: Torque is defined as the cross product of the position vector (from the axis to the point of force application) and the force vector: τ = r × F.
Q237. What are the conditions for a body to be in complete (static) equilibrium?
Ans: A body is in complete equilibrium when both the net force acting on it is zero (translational equilibrium) and the net torque acting on it is zero (rotational equilibrium).
Q238. Explain how a vector can be resolved into rectangular components.
Ans: A vector can be resolved into two perpendicular components (typically along the x and y axes) using trigonometry: the x-component is A cosθ and the y-component is A sinθ, where θ is the angle from the x-axis.
Q239. What is a unit vector, and why is it useful?
Ans: A unit vector has a magnitude of exactly one and indicates only direction; it is useful for expressing any vector as a magnitude multiplied by a unit vector in the desired direction.
Q240. Give one real-world example where the concept of torque is important.
Ans: Tightening a bolt with a wrench relies on torque, where a longer wrench handle (greater moment arm) allows the same force to produce a greater turning effect.
Q241. If two vectors are perpendicular to each other, what is the value of their dot product?
Ans: The dot product of two perpendicular vectors is zero, since cos90° = 0.
Q242. If two vectors are parallel to each other, what is the value of their cross product?
Ans: The cross product of two parallel vectors is zero, since sin0° = 0.
Q243. What is the difference between adding vectors and subtracting vectors graphically?
Ans: Adding vectors involves placing them head-to-tail and drawing the resultant from the start of the first to the end of the last; subtracting a vector is equivalent to adding its negative (reversed direction) vector.
Q244. Explain the significance of the right-hand rule in vector cross products.
Ans: The right-hand rule determines the direction of the cross product vector: if the fingers curl from the first vector toward the second, the extended thumb points in the direction of the resultant vector.
Q245. Why must both force and torque balance for a rigid body to remain in equilibrium?
Ans: If only force balances but torque does not, the body could still rotate; if only torque balances but force does not, the body could still accelerate linearly — both conditions are needed to prevent any motion.
Q246. Give an example of a physical situation where vector resolution is necessary to solve a problem.
Ans: Analyzing the motion of an object on an inclined plane requires resolving gravity into components parallel and perpendicular to the incline's surface.
🗂️ Unit 3: Translatory Motion
Q247. Differentiate between distance and displacement.
Ans: Distance is the total path length covered by an object (a scalar), while displacement is the shortest straight-line distance between initial and final positions, along with direction (a vector).
Q248. State Newton's three laws of motion in brief.
Ans: First Law: a body remains at rest or in uniform motion unless acted upon by an external force. Second Law: force equals the rate of change of momentum (F=ma for constant mass). Third Law: every action has an equal and opposite reaction.
Q249. What is the law of conservation of linear momentum?
Ans: In the absence of external forces, the total momentum of a system of interacting bodies remains constant before and after any interaction, such as a collision.
Q250. Differentiate between an elastic and an inelastic collision.
Ans: In an elastic collision, both momentum and kinetic energy are conserved; in an inelastic collision, momentum is conserved but kinetic energy is not (some is converted to heat, sound, or deformation).
Q251. Define impulse and state its relationship to momentum.
Ans: Impulse is the product of force and the time for which it acts (Impulse = F × t), and it equals the change in momentum produced by that force.
Q252. What is projectile motion, and what two independent components describe it?
Ans: Projectile motion is the curved path followed by an object launched into the air under gravity; it can be described by independent horizontal (constant velocity) and vertical (uniformly accelerated) components of motion.
Q253. At what angle of projection is the horizontal range of a projectile maximum, and why?
Ans: The range is maximum at a launch angle of 45°, because this angle provides the optimal balance between the horizontal and vertical components of the initial velocity.
Q254. Why does the horizontal component of a projectile's velocity remain constant throughout its flight (ignoring air resistance)?
Ans: Because gravity acts only vertically, there is no horizontal force to change the horizontal component of velocity, so it remains constant.
Q255. Write the three equations of uniformly accelerated motion.
Ans: v = u + at; s = ut + ½at²; v² = u² + 2as, where u is initial velocity, v is final velocity, a is acceleration, t is time, and s is displacement.
Q256. What information can be obtained from the slope of a velocity-time graph?
Ans: The slope of a velocity-time graph gives the acceleration of the object at that point in time.
Q257. What information can be obtained from the area under a velocity-time graph?
Ans: The area under a velocity-time graph gives the displacement of the object over that time interval.
Q258. Explain why a rocket can accelerate in the vacuum of space despite having nothing to push against.
Ans: According to Newton's Third Law, the rocket expels exhaust gases backward, and the reaction force pushes the rocket forward; this works even in a vacuum since it relies on the rocket-exhaust system's own momentum exchange, not on pushing against external air.
Q259. What is meant by 'uniformly accelerated motion'?
Ans: Uniformly accelerated motion is motion in which the acceleration of the body remains constant in both magnitude and direction throughout the motion.
Q260. How does the concept of momentum help explain the recoil of a gun when fired?
Ans: By conservation of momentum, the forward momentum gained by the bullet is balanced by an equal and opposite momentum gained by the gun, causing it to recoil backward.
Q261. Describe the motion of a ball thrown vertically upward, in terms of velocity and acceleration.
Ans: As the ball rises, its velocity decreases due to gravity acting downward, becoming zero at the highest point; it then accelerates downward as it falls, with acceleration remaining constant at g throughout (ignoring air resistance).
🗂️ Unit 4: Rotational and Circular Motion
Q262. Define angular velocity and state its relationship to linear velocity.
Ans: Angular velocity (ω) is the rate of change of angular displacement; it relates to linear velocity (v) by v = ωr, where r is the radius of the circular path.
Q263. What is centripetal acceleration, and in which direction does it act?
Ans: Centripetal acceleration is the acceleration of an object moving in a circular path, directed toward the center of the circle, with magnitude v²/r.
Q264. Define torque and state its SI unit.
Ans: Torque is the turning effect of a force about an axis, defined as the cross product of the position vector and force (τ = r × F); its SI unit is the Newton-metre (N·m).
Q265. What is moment of inertia, and what does it depend on?
Ans: Moment of inertia is a measure of a rotating body's resistance to change in its angular motion; it depends on the body's mass and how that mass is distributed relative to the axis of rotation.
Q266. State the law of conservation of angular momentum.
Ans: In the absence of external torque, the total angular momentum of a system remains constant.
Q267. Give a real-world example that demonstrates the conservation of angular momentum.
Ans: A figure skater spinning faster when pulling their arms inward demonstrates conservation of angular momentum, since reducing their moment of inertia increases their angular velocity to keep angular momentum constant.
Q268. Why is a road banked at curves?
Ans: Banking a road provides a component of the normal force directed toward the center of the curve, supplying additional centripetal force and reducing dependence on friction, allowing vehicles to turn safely at higher speeds.
Q269. What provides the centripetal force for a satellite orbiting the Earth?
Ans: The gravitational attraction between the Earth and the satellite provides the centripetal force necessary to keep the satellite in its circular (or elliptical) orbit.
Q270. Define angular momentum and state its formula.
Ans: Angular momentum is the rotational analogue of linear momentum, given by L = Iω, where I is the moment of inertia and ω is the angular velocity.
Q271. How does rotational kinetic energy differ from translational kinetic energy?
Ans: Translational kinetic energy (½mv²) is due to the linear motion of a body's center of mass, while rotational kinetic energy (½Iω²) is due to the body's rotation about an axis.
Q272. Explain why an object moving in uniform circular motion is still considered to be accelerating even though its speed is constant.
Ans: Although speed remains constant, the direction of velocity continuously changes, and since acceleration is defined as the rate of change of velocity (a vector), this direction change constitutes acceleration.
Q273. What is a geostationary satellite?
Ans: A geostationary satellite is one that orbits the Earth with a period exactly matching Earth's rotation (24 hours), so it appears to remain stationary relative to a fixed point on Earth's surface.
Q274. Explain what is meant by a 'couple' in the context of torque.
Ans: A couple consists of two equal, opposite, and parallel forces acting on a body along different lines of action, producing a pure turning effect (torque) without any net linear force.
Q275. How does the distribution of mass affect an object's moment of inertia?
Ans: Mass distributed farther from the axis of rotation contributes more to the moment of inertia than mass close to the axis, since moment of inertia depends on the square of the distance from the axis.
Q276. Why does a flywheel help maintain smooth, uniform rotational speed in machines?
Ans: A flywheel has a large moment of inertia, allowing it to store rotational kinetic energy and resist sudden changes in angular velocity, smoothing out fluctuations in a machine's speed.
🗂️ Unit 5: Work and Kinetic Energy
Q277. Define work done by a force and state its formula.
Ans: Work is done when a force causes a displacement, calculated as W = Fd cosθ, where F is force, d is displacement, and θ is the angle between them.
Q278. State the work-energy theorem.
Ans: The work-energy theorem states that the net work done on an object equals the change in its kinetic energy.
Q279. Differentiate between a conservative and a non-conservative force, with one example of each.
Ans: A conservative force's work is independent of the path taken (e.g., gravity), while a non-conservative force's work depends on the path taken (e.g., friction).
Q280. State the law of conservation of mechanical energy and the condition under which it holds.
Ans: The total mechanical energy (kinetic + potential) of a system remains constant, provided only conservative forces act on it, with no energy lost to friction or other non-conservative forces.
Q281. Define power and state its SI unit.
Ans: Power is the rate of doing work (or transferring energy), measured in watts (W), where one watt equals one joule per second.
Q282. Why is the work done by a force zero if the force is perpendicular to the displacement?
Ans: Because work depends on Fd cosθ, and when θ = 90°, cosθ = 0, so the work done is zero regardless of the force's magnitude.
Q283. Explain the difference between elastic and inelastic collisions in terms of kinetic energy.
Ans: In an elastic collision, total kinetic energy is conserved; in an inelastic collision, some kinetic energy is converted into other forms (like heat or sound), so total kinetic energy is not conserved.
Q284. What is elastic potential energy, and when is it stored?
Ans: Elastic potential energy is the energy stored in a deformed elastic object, such as a stretched or compressed spring, due to the work done in deforming it.
Q285. Explain why gravity is classified as a conservative force.
Ans: Gravity is conservative because the work done in moving an object between two points depends only on the vertical height difference, not on the specific path taken.
Q286. Define the efficiency of a machine and state its formula.
Ans: Efficiency is the ratio of useful output energy (or work) to the total input energy (or work), often expressed as a percentage: Efficiency = (Output/Input) × 100%.
Q287. Give one example of energy transformation in everyday life.
Ans: A falling object converts gravitational potential energy into kinetic energy as it falls; another example is a battery converting chemical energy into electrical energy.
Q288. Why does friction reduce the total mechanical energy of a moving system?
Ans: Friction is a non-conservative force that converts some of the system's kinetic energy into heat (thermal energy), which is not part of the mechanical energy, so total mechanical energy decreases.
Q289. Explain how the area under a force-displacement graph relates to work done.
Ans: The area under a force-displacement graph represents the work done by the force over that displacement, even when the force is variable.
Q290. A ball is dropped from a height and bounces back to a lower height each time. Explain this in terms of energy.
Ans: Each bounce involves some mechanical energy being converted to heat and sound due to the inelastic nature of the collision with the ground, so the ball has less mechanical energy (and thus a lower maximum height) after each bounce.
Q291. Why is 1 horsepower approximately equal to 746 watts important in practical engineering contexts?
Ans: This conversion allows engineers to compare the power output of engines and motors rated in horsepower (a traditional unit) directly with modern SI power ratings in watts.
🗂️ Unit 6: Fluid Mechanics
Q292. State Pascal's Law.
Ans: Pascal's Law states that pressure applied to an enclosed, incompressible fluid is transmitted equally and undiminished to every point of the fluid and to the walls of its container.
Q293. State Archimedes' Principle.
Ans: Archimedes' Principle states that the buoyant force on a submerged (or floating) object is equal to the weight of the fluid displaced by that object.
Q294. What is the equation of continuity, and what does it imply about fluid flow in a narrowing pipe?
Ans: The equation of continuity (A₁v₁ = A₂v₂) states that for an incompressible fluid, the product of cross-sectional area and velocity is constant; it implies that fluid speeds up as it flows through a narrower section of pipe.
Q295. State Bernoulli's principle in simple terms.
Ans: Bernoulli's principle states that for a flowing fluid, an increase in its speed is accompanied by a decrease in its pressure (and vice versa), consistent with conservation of energy along a streamline.
Q296. Why does a ship made of steel float, even though steel itself is denser than water?
Ans: The ship's hull design displaces a large volume of water; if the total weight of water displaced equals the ship's weight, the ship floats even though the material (steel) is denser than water.
Q297. Explain how an airplane wing generates lift using Bernoulli's principle.
Ans: Air moves faster over the curved top surface of the wing than beneath it, creating a region of lower pressure above the wing and higher pressure below, resulting in a net upward force (lift).
Q298. Differentiate between streamline (laminar) flow and turbulent flow.
Ans: Streamline flow is smooth and orderly, with fluid particles moving in parallel paths, while turbulent flow is chaotic and irregular, often involving eddies and unpredictable fluid motion.
Q299. Define viscosity and explain its physical significance.
Ans: Viscosity is a measure of a fluid's internal resistance to flow; higher viscosity fluids (like honey) flow more slowly and resist relative motion between layers more than lower viscosity fluids (like water).
Q300. Why does a person floating on their back in water sink more easily in a swimming pool than in the ocean?
Ans: Ocean water has a higher density than fresh pool water due to dissolved salt, providing greater buoyant force for the same displaced volume, making it easier to float.
Q301. What is the working principle of a hydraulic lift or hydraulic press?
Ans: A hydraulic lift works on Pascal's Law: a small force applied to a small-area piston creates pressure that is transmitted through the fluid to a larger-area piston, producing a much larger output force.
Q302. Explain the venturi effect and give one practical application.
Ans: The venturi effect occurs when fluid flows through a constriction, increasing its speed and decreasing its pressure, as explained by Bernoulli's principle; it is applied in devices like carburetors and venturi meters used to measure flow rate.
Q303. Why does perfume come out of an atomizer when air is squeezed through a narrow tube above the liquid?
Ans: The fast-moving air creates a region of low pressure above the tube (Bernoulli's principle), which draws the liquid perfume upward and allows it to be sprayed out with the airflow.
Q304. What determines whether an object floats, sinks, or remains suspended in a fluid?
Ans: An object floats if its average density is less than the fluid's density, sinks if its density is greater, and remains suspended (neutral buoyancy) if its density exactly equals the fluid's density.
Q305. Explain the term 'terminal velocity' in the context of an object falling through a viscous fluid.
Ans: Terminal velocity is the constant maximum speed reached by an object falling through a fluid when the upward viscous drag force (and buoyancy) balances the downward gravitational force, resulting in zero net acceleration.
Q306. Why is understanding fluid mechanics important in fields like aviation and civil engineering?
Ans: Fluid mechanics principles govern how air flows over aircraft (affecting lift and drag) and how water flows through pipes, dams, and irrigation systems, making it essential for designing safe and efficient structures and vehicles.
🗂️ Unit 7: Physics of Solids
Q307. Define stress and strain, along with their respective units.
Ans: Stress is force applied per unit area (measured in Pascals, same as pressure), while strain is the fractional change in dimension (dimensionless, as it is a ratio of similar quantities).
Q308. State Hooke's Law.
Ans: Hooke's Law states that, within the elastic limit, the stress produced in a material is directly proportional to the strain, i.e., stress ∝ strain.
Q309. Define Young's modulus and explain what a high value indicates about a material.
Ans: Young's modulus is the ratio of longitudinal stress to longitudinal strain; a high value indicates a stiff material that resists deformation strongly under an applied load, such as steel.
Q310. What is the difference between elastic and plastic deformation?
Ans: Elastic deformation is reversible — the material returns to its original shape once the deforming force is removed — while plastic deformation is permanent, with the material not returning to its original shape.
Q311. Differentiate between ductile and brittle materials, with one example of each.
Ans: Ductile materials (e.g., copper) undergo significant plastic deformation before breaking, while brittle materials (e.g., glass) break with little or no plastic deformation after the elastic limit is exceeded.
Q312. What information does the area under a stress-strain graph provide?
Ans: The area under a stress-strain graph represents the elastic (strain) energy stored per unit volume of the material for a given deformation.
Q313. Explain the significance of the elastic limit of a material.
Ans: The elastic limit is the maximum stress a material can withstand while still returning to its original shape upon removal of the force; beyond this point, permanent (plastic) deformation occurs.
Q314. Define the bulk modulus of a material.
Ans: Bulk modulus is the ratio of volumetric stress (pressure applied uniformly) to volumetric strain (fractional change in volume) of a material.
Q315. Why is steel preferred over rubber for constructing load-bearing structures like bridges?
Ans: Steel has a much higher Young's modulus (stiffness) than rubber, meaning it resists deformation under heavy loads far better, making it more suitable for structural applications requiring rigidity.
Q316. What is meant by 'fatigue' in materials, and why is it important in engineering design?
Ans: Fatigue refers to the weakening of a material due to repeated cyclic loading over time, which can cause failure at stress levels well below the material's normal breaking stress; engineers must account for this to prevent unexpected structural failure.
Q317. Explain the difference between tensile stress and compressive stress.
Ans: Tensile stress occurs when forces stretch or elongate a material, while compressive stress occurs when forces compress or shorten it.
Q318. What is shear strain, and how is it produced?
Ans: Shear strain is produced when a force is applied parallel (tangential) to a surface, causing layers of the material to slide relative to one another without necessarily changing volume.
Q319. Why does a longer wire of the same material and cross-section stretch more than a shorter wire under the same applied force?
Ans: Since strain (extension per original length) is the same for both wires under equal stress, a longer original length results in a proportionally larger absolute extension.
Q320. Describe what happens to a ductile material as it is stressed beyond its yield point.
Ans: Beyond the yield point, the material undergoes significant plastic (permanent) deformation, continuing to stretch or deform even without a large increase in applied stress, eventually leading to fracture.
Q321. Why is knowledge of stress and strain critical for engineers designing buildings, bridges, and vehicles?
Ans: Understanding stress and strain allows engineers to select appropriate materials and dimensions to ensure structures can safely withstand expected loads without exceeding their elastic limit or risking failure.
🗂️ Unit 8: Heat and Thermodynamics
Q322. State the first law of thermodynamics.
Ans: The first law of thermodynamics states that the change in internal energy of a system equals the heat added to the system minus the work done by the system (ΔU = Q − W), reflecting conservation of energy.
Q323. Differentiate between an isothermal process and an adiabatic process.
Ans: An isothermal process occurs at constant temperature, allowing heat exchange with surroundings, while an adiabatic process occurs with no heat exchange at all, though temperature may change.
Q324. What does the second law of thermodynamics say about the direction of heat flow?
Ans: The second law states that heat naturally flows from a hotter body to a colder body, and this process is irreversible unless external work is done (as in a refrigerator).
Q325. Define entropy and explain its general trend in natural processes.
Ans: Entropy is a measure of the disorder or randomness of a system; in natural (isolated) processes, the total entropy tends to increase over time, giving a direction to time.
Q326. Define specific heat capacity and state its formula.
Ans: Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree; it can be calculated as c = Q/(mΔT).
Q327. Differentiate between latent heat of fusion and latent heat of vaporization.
Ans: Latent heat of fusion is the heat required to change a substance from solid to liquid (or vice versa) at constant temperature, while latent heat of vaporization is the heat required to change a substance from liquid to gas (or vice versa) at constant temperature.
Q328. Explain the three modes of heat transfer.
Ans: Conduction is heat transfer through direct molecular collisions within a material; convection is heat transfer through the bulk movement of a fluid; radiation is heat transfer via electromagnetic waves, which can occur even through a vacuum.
Q329. What is the efficiency of a heat engine, and why can no heat engine be 100% efficient?
Ans: Efficiency is the ratio of useful work output to heat input; no heat engine can be 100% efficient because, according to the second law of thermodynamics, some heat must always be rejected to a cooler reservoir.
Q330. State the ideal gas equation and identify its variables.
Ans: The ideal gas equation is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the universal gas constant, and T is the absolute temperature.
Q331. According to kinetic theory, what does temperature represent at the molecular level?
Ans: Temperature represents a measure of the average kinetic energy of the particles (molecules) making up a substance.
Q332. Why does a refrigerator require external work input to transfer heat from its cold interior to the warmer room?
Ans: Since heat naturally flows from hot to cold, moving heat in the opposite direction (cold interior to warm room) requires external work input, consistent with the second law of thermodynamics.
Q333. Explain what is meant by a reversible process in thermodynamics.
Ans: A reversible process is an idealized process that can be reversed to restore both the system and its surroundings to their original states with no net change or loss; real processes are generally irreversible.
Q334. Why is the specific heat capacity of water considered unusually high, and what practical significance does this have?
Ans: Water's high specific heat capacity means it absorbs or releases a large amount of heat with relatively small temperature changes, which helps moderate coastal climates and makes water useful as a cooling agent in engines and industrial processes.
Q335. Describe the significance of the Carnot engine in thermodynamics.
Ans: The Carnot engine represents a theoretical, idealized heat engine that achieves the maximum possible efficiency between two given temperatures, serving as a benchmark against which real engines are compared.
Q336. Why does rapidly compressing air in a bicycle pump cause it to heat up, even without external heat being added?
Ans: This is an approximately adiabatic process — since compression happens quickly with little time for heat exchange, the work done in compressing the air increases its internal energy, raising its temperature.
🗂️ Unit 9: Waves
Q337. Differentiate between transverse and longitudinal waves, with one example of each.
Ans: In transverse waves, particle displacement is perpendicular to the wave's direction of travel (e.g., light waves); in longitudinal waves, particle displacement is parallel to the direction of travel (e.g., sound waves).
Q338. State the relationship between wave speed, frequency, and wavelength.
Ans: Wave speed equals the product of frequency and wavelength: v = fλ.
Q339. Define Simple Harmonic Motion (SHM) and state the key condition for a system to undergo SHM.
Ans: SHM is oscillatory motion in which the restoring force is directly proportional to the displacement from equilibrium and always directed toward that equilibrium position.
Q340. Explain the difference between constructive and destructive interference.
Ans: Constructive interference occurs when waves meet in phase, so their amplitudes add together, producing a larger resultant wave; destructive interference occurs when waves meet out of phase, causing their amplitudes to partially or fully cancel.
Q341. What are beats, and how is the beat frequency calculated?
Ans: Beats are periodic variations in loudness produced when two sound waves of slightly different frequencies superpose; the beat frequency equals the absolute difference between the two frequencies.
Q342. Define resonance and give one real-world example.
Ans: Resonance occurs when a system is driven at a frequency matching its natural frequency, resulting in a dramatic increase in amplitude; an example is a swing being pushed at just the right intervals to swing higher and higher.
Q343. What is the Doppler effect, and how does it explain the changing pitch of a passing ambulance siren?
Ans: The Doppler effect is the apparent change in frequency of a wave due to relative motion between source and observer; as an ambulance approaches, the sound waves are compressed, raising the pitch, and as it moves away, they stretch, lowering the pitch.
Q344. Differentiate between nodes and antinodes in a stationary (standing) wave.
Ans: Nodes are points of zero displacement in a stationary wave, while antinodes are points of maximum displacement.
Q345. Why can sound not travel through a vacuum, unlike light?
Ans: Sound is a mechanical wave that requires a material medium (solid, liquid, or gas) to propagate through particle vibrations, whereas light is an electromagnetic wave that can travel through a vacuum without any medium.
Q346. Explain how a stationary (standing) wave is formed.
Ans: A stationary wave is formed by the superposition of two identical waves of the same frequency and amplitude traveling in opposite directions, often due to reflection, resulting in a pattern of fixed nodes and antinodes.
Q347. At the extreme position of SHM, what are the values of velocity and acceleration of the oscillating particle?
Ans: At the extreme position, the velocity is zero, while the acceleration is at its maximum, directed toward the equilibrium position.
Q348. At the mean (equilibrium) position of SHM, what are the values of velocity and acceleration of the oscillating particle?
Ans: At the mean position, the velocity is at its maximum, while the acceleration is zero.
Q349. Explain the term 'damped oscillations' with an example.
Ans: Damped oscillations are oscillations whose amplitude gradually decreases over time due to resistive forces like friction or air resistance; a swinging pendulum that gradually comes to rest is a common example.
Q350. Why is the energy of a wave generally proportional to the square of its amplitude?
Ans: This relationship arises from the physics of oscillatory motion, where both kinetic and potential energy terms in a wave depend on the square of displacement (amplitude), so total energy scales with amplitude squared.
Q351. Give one practical application of the Doppler effect.
Ans: Traffic police radar guns use the Doppler effect to measure the speed of moving vehicles by detecting the shift in frequency of reflected radar waves.
🗂️ Unit 10: Electrostatics
Q352. State Coulomb's Law.
Ans: Coulomb's Law states that the electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
Q353. Define electric field intensity at a point.
Ans: Electric field intensity at a point is the force experienced by a unit positive test charge placed at that point, without disturbing the source charge distribution.
Q354. Define electric potential and state its SI unit.
Ans: Electric potential at a point is the work done per unit positive charge in bringing that charge from infinity to that point; its SI unit is the volt (V).
Q355. What is a capacitor, and define its capacitance.
Ans: A capacitor is a device used to store electric charge and energy; its capacitance is defined as the charge stored per unit potential difference across it (C = Q/V).
Q356. How does inserting a dielectric material between capacitor plates affect its capacitance?
Ans: Inserting a dielectric material generally increases the capacitance of a capacitor, since the dielectric reduces the effective electric field between the plates for a given charge.
Q357. Explain the difference between charging by conduction and charging by induction.
Ans: Charging by conduction involves direct contact between a charged object and a neutral object, transferring charge; charging by induction involves bringing a charged object near a neutral object without contact, causing a redistribution of charge.
Q358. Why is the electric field inside a charged conductor in electrostatic equilibrium always zero?
Ans: Because free charges within a conductor redistribute themselves until there is no net electric field inside; any internal field would cause further charge movement until equilibrium is reached.
Q359. Define equipotential surfaces and explain their relationship to electric field lines.
Ans: Equipotential surfaces are surfaces on which the electric potential is the same at every point; electric field lines are always perpendicular to equipotential surfaces.
Q360. How are capacitors combined differently in series versus parallel connections?
Ans: In series, the reciprocal of the equivalent capacitance equals the sum of the reciprocals of individual capacitances (resulting in a smaller equivalent capacitance); in parallel, the equivalent capacitance is simply the sum of the individual capacitances.
Q361. Explain the working principle of a lightning rod.
Ans: A lightning rod provides a path of low electrical resistance from the top of a building to the ground, attracting lightning strikes and safely conducting the charge to the ground, protecting the building from damage.
Q362. State Gauss's Law in simple terms.
Ans: Gauss's Law states that the total electric flux through any closed surface is directly proportional to the total electric charge enclosed within that surface.
Q363. What is an electric dipole?
Ans: An electric dipole consists of two equal and opposite point charges separated by a small distance, often characterized by a dipole moment.
Q364. Why does excess charge on an isolated conductor reside only on its outer surface?
Ans: Due to mutual repulsion between like charges, the charges move as far apart as possible, distributing themselves on the outer surface of the conductor rather than remaining within its volume.
Q365. Explain the energy stored in a charged capacitor and state its formula.
Ans: A charged capacitor stores electrical potential energy due to the separation of charge on its plates; this energy is given by U = ½CV², where C is capacitance and V is the potential difference across the plates.
Q366. Give one practical application of capacitors in everyday electronic devices.
Ans: Capacitors are used in camera flashes to store energy and release it quickly to produce a bright flash of light.
🗂️ Unit 11: Electricity
Q367. State Ohm's Law.
Ans: Ohm's Law states that, at constant temperature, the current through a conductor is directly proportional to the potential difference (voltage) across it: V = IR.
Q368. Define electrical resistance and state the factors it depends on.
Ans: Electrical resistance is the opposition offered by a conductor to the flow of current; it depends on the conductor's length, cross-sectional area, resistivity (material property), and temperature.
Q369. State Kirchhoff's Current Law (junction rule).
Ans: Kirchhoff's Current Law states that the sum of currents entering a junction in a circuit equals the sum of currents leaving that junction, reflecting conservation of charge.
Q370. State Kirchhoff's Voltage Law (loop rule).
Ans: Kirchhoff's Voltage Law states that the algebraic sum of potential differences around any closed loop in a circuit is zero, reflecting conservation of energy.
Q371. Differentiate between resistors connected in series and in parallel.
Ans: In series, resistors are connected end-to-end so the same current flows through each, and their resistances add directly; in parallel, resistors are connected across the same two points, sharing the total current, and the reciprocal of the equivalent resistance equals the sum of the reciprocals of individual resistances.
Q372. Define electromotive force (EMF) and distinguish it from terminal voltage.
Ans: EMF is the total energy supplied by a source per unit charge; terminal voltage is the actual potential difference available at the terminals of the source when current flows, which is less than the EMF due to the source's internal resistance.
Q373. Why should an ideal ammeter have very low resistance, while an ideal voltmeter should have very high resistance?
Ans: An ammeter is connected in series and should have low resistance so it does not significantly reduce the current being measured; a voltmeter is connected in parallel and should have high resistance so it draws minimal current, avoiding disturbance to the circuit being measured.
Q374. What is a superconductor, and what unique property does it exhibit?
Ans: A superconductor is a material that, below a certain critical temperature, exhibits zero electrical resistance, allowing current to flow without any energy loss due to resistance.
Q375. Explain the purpose of a fuse in an electrical circuit.
Ans: A fuse is a safety device containing a thin wire that melts and breaks the circuit when the current exceeds a safe limit, protecting the circuit and connected appliances from damage due to excessive current.
Q376. Why are household appliances typically connected in parallel rather than in series?
Ans: Parallel connections allow each appliance to operate independently at the full supply voltage, so if one appliance is switched off or fails, the others continue to function normally, unlike a series connection where all devices would be affected.
Q377. Define electrical power and state two formulas used to calculate it.
Ans: Electrical power is the rate at which electrical energy is converted or consumed; it can be calculated using P = VI or P = I²R.
Q378. How does the resistance of a semiconductor typically change with increasing temperature, and how does this differ from a typical metal?
Ans: For most semiconductors, resistance decreases as temperature increases, whereas for most pure metals, resistance increases with increasing temperature.
Q379. Explain the concept of drift velocity in the context of electric current.
Ans: Drift velocity is the slow net velocity gained by free electrons in a conductor due to an applied electric field, superimposed on their much faster random thermal motion; it is this net drift that constitutes the electric current.
Q380. Why is a potentiometer considered more accurate than a simple voltmeter for measuring EMF?
Ans: A potentiometer measures EMF without drawing any current from the source being measured (at balance point), avoiding the voltage drop caused by internal resistance that affects voltmeter readings.
Q381. Explain what happens during a short circuit and why it can be dangerous.
Ans: A short circuit occurs when current finds an unintended path of very low resistance, causing an abnormally high current to flow, which can generate excessive heat, potentially damaging equipment or causing a fire.
🗂️ Unit 12: Magnetism
Q382. State the formula for the magnetic force on a moving charge in a magnetic field.
Ans: The magnetic force is given by F = qvB sinθ, where q is the charge, v is its velocity, B is the magnetic field strength, and θ is the angle between velocity and field; the direction is given by F = qv × B using the right-hand rule.
Q383. State Faraday's Law of electromagnetic induction.
Ans: Faraday's Law states that the induced EMF in a circuit is directly proportional to the rate of change of magnetic flux through the circuit.
Q384. State Lenz's Law and explain the physical principle it reflects.
Ans: Lenz's Law states that the direction of an induced current is such that it opposes the change in magnetic flux that produced it; this reflects the principle of conservation of energy.
Q385. Differentiate between a step-up and a step-down transformer.
Ans: A step-up transformer increases voltage (and decreases current) from primary to secondary coil, while a step-down transformer decreases voltage (and increases current).
Q386. Define self-inductance and mutual inductance.
Ans: Self-inductance is a coil's ability to induce an EMF in itself due to a change in its own current; mutual inductance is the ability of a changing current in one coil to induce an EMF in a neighboring coil.
Q387. What are eddy currents, and how are they minimized in transformer cores?
Ans: Eddy currents are circulating currents induced within the bulk of a conductor due to changing magnetic flux; they are minimized in transformer cores by using thin, laminated, insulated sheets of iron instead of a solid core.
Q388. Explain the working principle of an electric motor.
Ans: An electric motor converts electrical energy into mechanical energy using the magnetic force exerted on a current-carrying coil placed within a magnetic field, causing the coil to rotate.
Q389. Explain the working principle of an electric generator.
Ans: An electric generator converts mechanical energy into electrical energy by rotating a coil within a magnetic field, inducing an EMF through electromagnetic induction (Faraday's Law).
Q390. Differentiate between diamagnetic and ferromagnetic materials.
Ans: Diamagnetic materials are weakly repelled by an external magnetic field and show no permanent magnetization, while ferromagnetic materials are strongly attracted and can retain magnetization even after the external field is removed.
Q391. What is the Hall effect, and what practical information can it provide?
Ans: The Hall effect is the generation of a transverse voltage across a current-carrying conductor placed in a magnetic field; it can be used to determine the sign and density of charge carriers in a material.
Q392. Explain how a moving coil galvanometer detects electric current.
Ans: A moving coil galvanometer works because a current-carrying coil placed in a magnetic field experiences a torque proportional to the current, causing the coil (and an attached pointer) to deflect by an amount related to the current's magnitude.
Q393. Why do two parallel wires carrying current in the same direction attract each other?
Ans: Each current-carrying wire produces its own magnetic field, and the magnetic force experienced by the other wire (carrying current in the same direction) within that field results in an attractive force between them.
Q394. Describe how a solenoid produces a magnetic field, and where the field is most uniform.
Ans: A solenoid is a long coil of wire; when current flows through it, it produces a magnetic field that is strongest and most uniform inside the solenoid, parallel to its axis.
Q395. Explain, using Lenz's Law, what happens when a magnet is pushed into a coil of wire.
Ans: As the magnet is pushed into the coil, the changing magnetic flux induces a current in the coil; according to Lenz's Law, this induced current creates a magnetic field that opposes the magnet's motion, effectively repelling it and resisting the change.
Q396. Why has a magnetic monopole never been observed, and what does this imply about magnets?
Ans: Despite theoretical predictions in some models, no isolated single magnetic pole (monopole) has ever been conclusively observed; this implies that magnets always occur with paired north and south poles that cannot be separated.
🗂️ Unit 13: Relativity
Q397. State the two postulates of Einstein's Special Theory of Relativity.
Ans: First, the laws of physics are the same in all inertial (non-accelerating) reference frames; second, the speed of light in vacuum is the same for all observers, regardless of the motion of the source or observer.
Q398. Define time dilation as predicted by Special Relativity.
Ans: Time dilation is the phenomenon in which a clock moving relative to an observer is measured by that observer to run slower than a clock at rest relative to them.
Q399. Define length contraction as predicted by Special Relativity.
Ans: Length contraction is the phenomenon in which the length of a moving object, measured in the direction of motion by a stationary observer, appears shorter than its length when at rest (proper length).
Q400. State Einstein's mass-energy equivalence relation and explain its significance.
Ans: The relation E = mc² states that mass and energy are equivalent and interconvertible; it implies that even a small amount of mass corresponds to a very large amount of energy, since c (the speed of light) is an extremely large number.
Q401. Why must GPS satellite clocks be corrected for relativistic effects?
Ans: GPS satellites move at high speed relative to Earth's surface (causing time dilation) and experience weaker gravity at altitude (a General Relativity effect); both effects alter their clock rates, and without correction, positioning calculations would be significantly inaccurate.
Q402. Explain the 'twin paradox' and what it illustrates about relativity.
Ans: The twin paradox describes a scenario where one twin travels at high (relativistic) speed on a journey and returns younger than the twin who stayed on Earth, illustrating that time dilation is a real physical effect depending on relative motion.
Q403. What was the significance of the Michelson-Morley experiment in the development of relativity?
Ans: The Michelson-Morley experiment failed to detect the expected motion of Earth through a hypothesized 'luminiferous ether,' providing strong evidence against the ether's existence and helping motivate Einstein's postulate of the constant speed of light.
Q404. Why can no object with mass be accelerated to the speed of light, according to Special Relativity?
Ans: As an object's speed approaches the speed of light, the energy required to further accelerate it increases without bound (approaching infinity), making it impossible to reach or exceed the speed of light with a finite amount of energy.
Q405. Explain why simultaneity is considered 'relative' rather than absolute in Special Relativity.
Ans: Two events that appear simultaneous to one observer may not appear simultaneous to another observer moving relative to the first, because the finite speed of light and relative motion affect how and when each observer perceives the events.
Q406. What is meant by an object's 'rest energy'?
Ans: Rest energy is the intrinsic energy an object possesses due to its mass alone, even when it is not moving, given by E₀ = mc².
Q407. How does General Relativity describe gravity differently from Newtonian physics?
Ans: General Relativity describes gravity not as a force acting at a distance, but as the curvature of spacetime caused by the presence of mass and energy, with objects moving along paths determined by this curvature.
Q408. Give one experimentally confirmed prediction of General Relativity.
Ans: The bending of starlight around massive objects like the Sun (gravitational lensing), first confirmed during a solar eclipse observation, is a key experimentally confirmed prediction of General Relativity.
Q409. Why do muons created in the upper atmosphere manage to reach the Earth's surface despite their very short lifetimes?
Ans: Muons travel at speeds close to the speed of light, and due to time dilation, their lifetime as measured from Earth's reference frame is extended enough for many of them to survive the journey to the surface.
Q410. Explain the concept of 'spacetime' as introduced in relativity.
Ans: Spacetime is the unification of the three dimensions of space with the one dimension of time into a single four-dimensional continuum, within which all physical events occur and are described.
Q411. Why is relativistic momentum different from classical (Newtonian) momentum at high speeds?
Ans: Relativistic momentum includes a factor that increases without bound as an object's speed approaches the speed of light, unlike classical momentum (mv), which would incorrectly predict momentum increasing linearly without limit even beyond light speed.
🗂️ Unit 14: Particle Physics
Q412. According to the Standard Model, what are the two basic categories of fundamental matter particles?
Ans: The two basic categories are quarks (which combine to form particles like protons and neutrons) and leptons (such as electrons and neutrinos).
Q413. Describe the quark composition of a proton and a neutron.
Ans: A proton consists of two up quarks and one down quark, while a neutron consists of one up quark and two down quarks.
Q414. Name the four fundamental forces of nature.
Ans: The four fundamental forces are the gravitational force, electromagnetic force, strong nuclear force, and weak nuclear force.
Q415. What is the role of the strong nuclear force in atomic nuclei?
Ans: The strong nuclear force binds quarks together within protons and neutrons, and also binds protons and neutrons together within the nucleus, overcoming the electrostatic repulsion between protons.
Q416. What is an antiparticle, and what happens when a particle meets its antiparticle?
Ans: An antiparticle has the same mass as its corresponding particle but opposite charge (and certain other opposite properties); when a particle and its antiparticle meet, they annihilate each other, converting their mass into energy, typically in the form of photons.
Q417. Name the force-carrying particle (boson) associated with the electromagnetic force.
Ans: The photon is the force-carrying particle associated with the electromagnetic force.
Q418. What is the significance of the Higgs boson, discovered in 2012?
Ans: The Higgs boson is associated with the mechanism by which fundamental particles acquire mass, confirming a key prediction of the Standard Model of particle physics.
Q419. Explain what CP-violation is and why it is significant.
Ans: CP-violation is a phenomenon where the combined symmetry of charge conjugation (C) and parity (P) is not perfectly obeyed in certain particle decays; it is significant because it helps explain why the universe is dominated by matter rather than containing equal amounts of matter and antimatter.
Q420. What does 'color confinement' mean in the context of quarks?
Ans: Color confinement refers to the property that quarks are never found in isolation in nature; they are always confined within composite particles like protons, neutrons, or mesons due to the strong nuclear force.
Q421. Differentiate between baryons and mesons.
Ans: Baryons (such as protons and neutrons) are composed of three quarks, while mesons are composed of a quark and an antiquark pair.
Q422. What is a neutrino, and why is it difficult to detect?
Ans: A neutrino is an electrically neutral lepton with an extremely small mass that interacts only very weakly with matter, making it very difficult to detect since it can pass through large amounts of matter without interacting.
Q423. According to the Big Bang theory, approximately how old is the universe, and what does particle physics contribute to understanding its early stages?
Ans: The universe is estimated to be about 13.7 billion years old; particle physics helps explain the fundamental processes, such as the formation of matter and antimatter and their asymmetry, that occurred in the earliest fractions of a second after the Big Bang.
Q424. What is the purpose of particle accelerators such as the Large Hadron Collider (LHC)?
Ans: Particle accelerators collide particles at extremely high energies, allowing scientists to study fundamental particles, forces, and phenomena that are not observable under normal conditions, such as the Higgs boson.
Q425. Give an example of a practical application arising from particle physics research.
Ans: Technologies such as radiation therapy for cancer treatment and medical imaging techniques (like PET scans) have developed from particle physics research.
Q426. Why is the study of matter-antimatter asymmetry considered essential to our existence?
Ans: If matter and antimatter had been created in perfectly equal amounts during the Big Bang, they would have completely annihilated each other, leaving an empty universe; the slight excess of matter (due to CP-violation) is essential for the existence of stars, planets, and life.
