Q50. A planet takes eight Earth years to orbit the Sun once. Compared with Earth’s orbit, what is the semimajor axis of this planet’s orbit?
[UPSC NDA-I, 12 Apr 2026]
(A) The same
(B) Twice as large
(C) Three times as large
(D) Four times as large
Answer: (D) Four times as large
Explanation: Kepler’s third law states that orbital period squared is proportional to semimajor axis cubed for planets orbiting the same star. With period ratio eight, the axis ratio is 8 to the power two-thirds, which equals four.
Q49. For a particle moving under forces, the total work done depends on its initial and final speeds. Which statement follows?
[UPSC NDA-I, 12 Apr 2026]
(A) The force must be conservative
(B) The net work equals the change in kinetic energy
(C) The force must remain constant
(D) Its velocity must always increase
Answer: (B) The net work equals the change in kinetic energy
Explanation: The work–energy theorem gives net work as one-half the mass multiplied by final speed squared minus initial speed squared. This applies even when forces vary or include friction. It does not imply that each individual force is conservative or constant.
Q48. Which condition ensures stable equilibrium for a floating body?
[UPSC NDA-I, 12 Apr 2026]
(A) Its centre of gravity lies above its centre of buoyancy
(B) Its centre of gravity lies below its centre of buoyancy
(C) Its centre of gravity coincides with its centre of buoyancy
(D) Its centre of gravity lies below its metacentre
Answer: (D) Its centre of gravity lies below its metacentre
Explanation: When a floating object tilts slightly, the buoyancy line shifts. If the metacentre is above the centre of gravity, the buoyant force and weight generate a restoring couple. This metacentric condition determines stability, not the buoyancy-centre position alone.
Q47. Why is a person landing on soft sand less likely to suffer injury than someone landing on a hard surface?
[UPSC NDA-I, 12 Apr 2026]
(A) Sand exerts no reaction force
(B) Sand reduces the change in momentum
(C) Sand lengthens the impact time
(D) Sand increases the person’s momentum
Answer: (C) Sand lengthens the impact time
Explanation: The person must lose nearly the same downward momentum whether landing on sand or concrete. Soft sand deforms and extends the stopping time. Since average impact force equals change in momentum divided by time, the longer interval produces a smaller force.
Q46. Which statement correctly expresses Newton’s second law of motion?
[UPSC CDS-I, 12 Apr 2026]
(A) Rate of change of angular momentum equals applied force
(B) Rate of change of displacement is proportional to applied force
(C) Rate of change of acceleration is proportional to applied force
(D) Rate of change of linear momentum equals the applied force
Answer: (D) Rate of change of linear momentum equals the applied force
Explanation: Newton’s second law relates the resultant external force to the time rate of change of linear momentum. For constant mass, differentiating momentum mv gives F = ma. Angular momentum instead changes under torque, so the first choice confuses two different physical relationships.
Q45. What is the property of a body that makes it resist changes to its state of rest or uniform motion in a straight line?
[RRB NTPC Graduate, 25 Mar 2026]
(A) Acceleration
(B) Momentum
(C) Force
(D) Inertia
Answer: (D) Inertia
Explanation: Inertia is the tendency of matter to preserve its existing motion unless a net external force acts. Newton’s first law describes this behaviour. Mass measures translational inertia: an object with greater mass generally needs a greater force for the same acceleration.
Q44. Which expression represents the SI unit of linear momentum?
[RRB NTPC Graduate, 22 Mar 2026]
(A) g m s⁻¹
(B) kg m s⁻²
(C) kg m s
(D) kg m s⁻¹
Answer: (D) kg m s⁻¹
Explanation: Momentum equals mass multiplied by velocity. In SI, mass uses kilograms and velocity uses metres per second, making kg m s⁻¹ the correct unit. The unit kg m s⁻² belongs to force, the newton, rather than momentum.
Q43. If the separation between two masses is doubled while the masses stay constant, what happens to their gravitational force?
[RRB Group D, 27 Dec 2025]
(A) It doubles
(B) It becomes four times larger
(C) It becomes half
(D) It becomes one-fourth
Answer: (D) It becomes one-fourth
Explanation: Newton’s universal gravitation law states that force varies inversely with the square of separation. Doubling the distance changes its square by a factor of four, so the mutual gravitational attraction becomes one-quarter of its previous value, assuming masses are unchanged.
Q42. An unbalanced net force acting on a moving object can directly change which quantity?
[RRB Group D, 26 Dec 2025]
(A) Density
(B) Mass
(C) Time
(D) Velocity
Answer: (D) Velocity
Explanation: A net external force produces acceleration under Newton’s second law. Acceleration represents a change in velocity, either its size, its direction, or both. A force does not automatically change an object’s mass or density, and time is not the motion variable affected.
Q41. When the masses of both attracting bodies are doubled but their separation is unchanged, what is the gravitational force?
[RRB Group D, 23 Dec 2025]
(A) Twice the original
(B) Four times the original
(C) Eight times the original
(D) Half the original
Answer: (B) Four times the original
Explanation: According to universal gravitation, force is proportional to the product of the two masses. Doubling each mass makes this product four times larger: (2m₁)(2m₂) = 4m₁m₂. Since the distance is unchanged, the attraction increases fourfold.
