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Question 1. Which of the following instruments is best suited for measuring the period of a simple pendulum with high precision? A) Ruler B) Stopwatch C) Photogate timer D) Vernier caliper Answer: C Explanation: A photogate timer detects the interruption of a light beam by the pendulum bob, providing timing resolution much finer than a manual stopwatch. Question 2. In an experiment, the independent variable is the mass of a cart, while the dependent variable is its acceleration down an incline. Which quantity is a controlled variable? A) The incline angle B) The measured acceleration C) The cart’s velocity D) The friction coefficient Answer: A Explanation: The incline angle must be kept constant to ensure that changes in acceleration are due only to changes in mass. Question 3. The number of significant figures in the result of a calculation should be limited by: A) The number with the most significant figures B) The number with the fewest significant figures C) The average of significant figures of all numbers D) The number with the largest exponent Answer: B Explanation: In multiplication or division, the result cannot have more significant figures than the input with the fewest.
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Question 4. A log-log plot of data yields a straight line with slope 2. Which power-law relationship best describes the underlying variables? A) y ∝ x B) y ∝ x² C) y ∝ √x D) y ∝ x⁻¹ Answer: B Explanation: In a log-log plot, the slope equals the exponent of the power-law relation; a slope of 2 means y ∝ x². Question 5. Which historical figure first formulated the law of universal gravitation? A) Galileo Galilei B) Isaac Newton C) James Clerk Maxwell D) Albert Einstein Answer: B Explanation: Newton’s law of universal gravitation (1687) described the inverse-square force between any two masses. Question 6. The vector sum of two forces F₁ = 4 N at 0° and F₂ = 3 N at 90° is: A) 5 N at 36.9° B) 7 N at 45° C) 1 N at 0° D) 4 N at 90° Answer: A Explanation: Using the Pythagorean theorem, resultant magnitude = √(4²+3²)=5 N; angle = tan⁻¹(3/4)=36.9°.
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A) Doubles B) Halves C) Remains the same D) Increases by √ Answer: C Explanation: sin 2θ = sin 60° = sin 120°; both equal √3/2, so range is unchanged. Question 10. The slope of a velocity-time graph represents: A) Displacement B) Acceleration C) Force D) Momentum Answer: B Explanation: Slope = Δv/Δt = acceleration. Question 11. According to Newton’s third law, when a book rests on a table, the normal force exerted by the table on the book is: A) Equal to the book’s weight and opposite in direction B) Greater than the book’s weight C) Zero because the book is not moving D) Dependent on the coefficient of friction Answer: A Explanation: The table exerts an upward normal force equal in magnitude and opposite to the downward gravitational force. Question 12. A block of mass 2 kg slides down a frictionless incline of height 5 m. Its speed at the bottom is: A) 5 m/s B) 7 m/s
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C) 10 m/s D) 14 m/s Answer: B Explanation: Using conservation of energy: mgh = ½ mv² → v = √(2gh) = √(2·9.8·5) ≈ 9.9 m/s (Wait compute). Actually √(98) ≈ 9.9 m/s, not in options. Adjust options: A) 7 m/s B) 9.9 m/s C) 11 m/s D) 14 m/s Answer: B Explanation: v = √(2·9.8·5) ≈ 9.9 m/s. Question 13. The work done by a constant force of 20 N acting at 30° to the displacement of 5 m is: A) 50 J B) 86.6 J C) 100 J D) 173.2 J Answer: B Explanation: Work = F·d·cosθ = 20·5·cos30° = 100·0.866 = 86.6 J. Question 14. A perfectly elastic collision between two identical billiard balls results in: A) Both balls stop moving B) The first ball stops, the second moves with original speed C) Both balls move together with half the original speed D) The first ball rebounds with same speed, second remains at rest Answer: B
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80.91e-3 = 0.0809 N·m². Divide by r² = 0.04 → 2.0225 N attractive. So answer should be 2.0 N attractive. Thus correct option: A. Question 18. The electric field a distance r from an infinite line charge with linear charge density λ is given by E = (λ)/(2πϵ₀r). If λ doubles, the field at a fixed r: A) Doubles B) Halves C) Remains unchanged D) Quadruples Answer: A Explanation: E is directly proportional to λ. Question 19. In a series circuit with three resistors of 2 Ω, 4 Ω, and 6 Ω connected to a 12 V battery, the current through the 4 Ω resistor is: A) 0.5 A B) 1 A C) 1.5 A D) 2 A Answer: B Explanation: Total resistance = 12 Ω; I = V/R = 12/12 = 1 A; same current flows through each series resistor. Question 20. A capacitor of capacitance 10 μF is charged to 100 V. Its stored energy is: A) 0.05 J B) 0.5 J C) 5 J D) 50 J
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Answer: B Explanation: U = ½ CV² = 0.5·10×10⁻⁶·(100)² = 0.5·10⁻⁵·10⁴ = 0.5 J. Question 21. Kirchhoff’s loop rule applied to a simple circuit containing a 9 V battery and two resistors (3 Ω and 6 Ω) in series predicts the voltage drop across the 6 Ω resistor to be: A) 3 V B) 6 V C) 9 V D) 12 V Answer: B Explanation: Current I = 9 V/(3+6) Ω = 1 A; voltage across 6 Ω = I·R = 6 V. Question 22. The magnetic field at the center of a circular loop of radius 0.1 m carrying a current of 5 A is: A) 1.0 × 10⁻⁶ T B) 1.0 × 10⁻⁴ T C) 1.0 × 10⁻³ T D) 1.0 × 10⁻² T Answer: C Explanation: B = μ₀I/(2R) = (4π×10⁻⁷)(5)/(0.2) ≈ 3.14×10⁻³ T ≈ 1.0×10⁻³ T (choice C). Question 23. According to the right-hand rule for a straight current-carrying wire, the magnetic force on a positive charge moving upward through a magnetic field directed into the page is: A) To the left B) To the right C) Upward D) Downward
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Explanation: λ = v/f = 500/250 = 2 m? Wait compute: 500/250 = 2 m. Option C is 2.0 m. So answer C. Question 27. The phenomenon where waves bend around a small obstacle is called: A) Reflection B) Refraction C) Diffraction D) Interference Answer: C Explanation: Diffraction is the bending of waves around obstacles or through apertures. Question 28. Two coherent light sources produce an interference pattern on a screen. If the wavelength is doubled while all other parameters remain unchanged, the fringe spacing will: A) Halve B) Double C) Remain the same D) Become zero Answer: B Explanation: Fringe spacing Δy = λL/d; directly proportional to wavelength. Question 29. The Doppler shift for a source moving away from a stationary observer is a: A) Increase in frequency (blue shift) B) Decrease in frequency (red shift) C) No change in frequency D) Increase in amplitude Answer: B
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Explanation: Receding source stretches the wavefronts, lowering observed frequency. Question 30. Snell’s law relates the angles of incidence and refraction to the indices of refraction. If light passes from air (n≈1) into glass (n≈1.5) at an incidence angle of 30°, the angle of refraction is approximately: A) 19.5° B) 30° C) 41.8° D) 45° Answer: A Explanation: n₁ sinθ₁ = n₂ sinθ₂ → sinθ₂ = (1/1.5)·sin30° = (0.6667)(0.5)=0. → θ₂≈19.5°. Question 31. A converging lens forms a real image that is twice the size of the object. The image distance is: A) Equal to the focal length B) Twice the focal length C) Half the focal length D) Three times the focal length Answer: B Explanation: For a magnification |m| = |v/u| = 2 and real image → v = 2u. Lens equation 1/f = 1/u + 1/v gives v = 2f. Question 32. The critical angle for total internal reflection at a water-air interface (n_water=1.33) is: A) 48.6° B) 61.0° C) 71.8° D) 90° Answer: B
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Explanation: Boyle’s law: P₁V₁ = P₂V₂ → V₂ = (1 atm·2 L)/3 atm = 0.667 L? Wait compute: P₁=1 atm? Not given. Use initial pressure P₁ unknown; but ratio V₂/V₁ = P₁/P₂. Assuming initial pressure 1 atm, V₂ = 2 L·(1/3)=0.667 L (not listed). Let's assume initial pressure 2 atm? Not clear. We'll adjust numbers: Suppose initial pressure 1 atm. Then answer 0.67 L (not in list). Replace options: A) 0.67 L B) 1.0 L C) 2.0 L D) 3.0 L Answer: A Explanation: Using P₁V₁ = P₂V₂ → V₂ = (1 atm·2 L)/3 atm = 0.67 L. Question 36. The first law of thermodynamics is a statement of: A) Conservation of momentum B) Conservation of energy C) Increase of entropy D) Absolute zero Answer: B Explanation: ΔU = Q – W expresses energy conservation for a system. Question 37. In an isothermal expansion of an ideal gas, the work done by the gas is: A) Zero B) Positive and equal to ΔU C) Positive and equal to nRT ln(V₂/V₁) D) Negative Answer: C Explanation: For isothermal process, W = ∫PdV = nRT ln(V₂/V₁).
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Question 38. The efficiency of a Carnot engine operating between 500 K and 300 K is: A) 40% B) 60% C) 70% D) 80% Answer: A Explanation: η = 1 – T_c/T_h = 1 – 300/500 = 0.4 → 40%. Question 39. The entropy change when 1 mol of an ideal gas expands reversibly from 1 L to 2 L at 298 K is: A) 5.76 J/K B) 8.31 J/K C) 11.5 J/K D) 0 J/K Answer: A Explanation: ΔS = nR ln(V₂/V₁) = (1 mol)(8.314 J/mol·K)·ln2 ≈ 5.76 J/K. Question 40. In special relativity, an object moving at 0.8c experiences time dilation factor γ equal to: A) 1. B) 1. C) 1. D) 2. Answer: C Explanation: γ = 1/√(1–v²/c²) = 1/√(1–0.64) = 1/√0.36 = 1/0.6 = 1.667. Question 41. The relativistic kinetic energy of a particle with rest mass m₀ traveling at 0.6c is: A) 0.2 m₀c²
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Answer: C Explanation: r_n = n²a₀; a₀ = 0.053 nm → r₃ = 9·0.053 nm = 0.477 nm. Question 45. The first excited state of a hydrogen atom emits a photon with wavelength approximately: A) 121.6 nm (Lyman-α) B) 656.3 nm (Balmer-α) C) 434.0 nm (Balmer-γ) D) 10.2 eV Answer: A Explanation: Transition from n=2 to n=1 gives Lyman-α line at 121.6 nm. Question 46. The half-life of a radioactive isotope is 10 years. After 30 years, the remaining fraction of the original sample is: A) 1/ B) 1/ C) 1/ D) 1/ Answer: C Explanation: After 3 half-lives, (1/2)³ = 1/8 remains. Question 47. In a nuclear fission reaction, the mass defect is converted to energy according to: A) E = mc² B) E = mgh C) E = ½ mv² D) E = qV Answer: A
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Explanation: Mass–energy equivalence relates lost mass Δm to released energy ΔE = Δm c². Question 48. The neutron capture cross-section of a material is a measure of: A) Its electrical conductivity B) Its probability of absorbing a neutron C) Its magnetic permeability D) Its thermal expansion coefficient Answer: B Explanation: Cross-section quantifies the likelihood of a nuclear interaction such as neutron capture. Question 49. The speed of light in a vacuum is: A) 3.00 × 10⁶ m/s B) 3.00 × 10⁷ m/s C) 3.00 × 10⁸ m/s D) 3.00 × 10⁹ m/s Answer: C Explanation: Defined constant c = 2.998 × 10⁸ m/s. Question 50. Which of the following is a scalar quantity? A) Force B) Momentum C) Acceleration D) Temperature Answer: D Explanation: Temperature has magnitude only; the others are vectors.
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Question 54. The acceleration of a car that increases its speed from 0 to 25 m/s in 5 s is: A) 2 m/s² B) 5 m/s² C) 10 m/s² D) 25 m/s² Answer: A Explanation: a = Δv/Δt = 25/5 = 5 m/s² (Oops that's 5). So answer B. Question 55. In a uniform circular motion of radius 0.5 m with speed 4 m/s, the centripetal acceleration is: A) 8 m/s² B) 16 m/s² C) 32 m/s² D) 64 m/s² Answer: B Explanation: a_c = v²/r = 16/0.5 = 32 m/s² (Wait compute: v² = 16, divide by 0. → 32). So answer C. Question 56. The work done by gravity when a 2 kg object falls 3 m vertically downward is: A) –58.8 J B) 0 J C) 58.8 J D) –19.6 J Answer: C Explanation: Work = mgh = 2·9.8·3 = 58.8 J (positive since force and displacement are in same direction).
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Question 57. A 0.5 kg ball is attached to a spring (k = 200 N/m) and pulled 0.1 m from equilibrium. Its maximum kinetic energy during oscillation is: A) 0.5 J B) 1 J C) 2 J D) 5 J Answer: B Explanation: Elastic potential at max displacement = ½ k x² = 0.5·200·0.01 = 1 J; this converts to kinetic energy at equilibrium. Question 58. The impulse imparted to a 3 kg object that changes its velocity from 2 m/s to 8 m/s is: A) 6 Ns B) 12 Ns C) 18 Ns D) 24 Ns Answer: C Explanation: Impulse = Δp = mΔv = 3·6 = 18 Ns. Question 59. In a perfectly inelastic collision, two cars of masses 1000 kg and 1500 kg travel at 20 m/s and 10 m/s respectively in the same direction and stick together. Their final speed is: A) 12 m/s B) 14 m/s C) 16 m/s D) 18 m/s Answer: B Explanation: Conservation of momentum: (1000·20 + 1500·10)/(2500) = (20000+15000)/2500 = 35000/2500 = 14 m/s.
