Q30. A planet moves around the Sun in a circular orbit of radius r. What work does gravity perform as it moves through half the orbit?
[WBCS Prelims, 2024]
(A) Zero
(B) F × 2πr
(C) F × πr
(D) F × 2r
Answer: (A) Zero
Explanation: For circular motion, gravitational force points radially towards the Sun, while the instantaneous displacement is tangential to the orbit. Force and displacement remain perpendicular, so their dot product and the work done are zero throughout the half revolution.
Q29. If fluid density is ρ, velocity is v, lift coefficient is Cₗ and projected area is A, what is the lift force?
[MPPSC Assistant Engineer (Civil), 8 Oct 2023]
(A) ½ρv²Cₗ
(B) ½ρv²CₗA
(C) 2ρv²CₗA
(D) ρv²CₗA
Answer: (B) ½ρv²CₗA
Explanation: Aerodynamic lift is expressed through dynamic pressure, one-half density times speed squared, multiplied by projected area and the dimensionless lift coefficient. Thus L = ½ρv²CₗA. Omitting area would give incorrect physical dimensions for a force.
Q28. When a stone is thrown upward, what energy conversion takes place as it rises?
[SSC MTS, 12 Sep 2023 (Shift 3)]
(A) Kinetic energy changes into mechanical energy
(B) Potential energy changes into gravitational energy
(C) Mechanical energy changes into kinetic energy
(D) Kinetic energy changes into gravitational potential energy
Answer: (D) Kinetic energy changes into gravitational potential energy
Explanation: During ascent, gravity reduces the stone’s speed while its height increases. Its kinetic energy gradually converts to gravitational potential energy. At the highest point, its instantaneous speed is zero, so the initial kinetic energy has become potential energy, neglecting air resistance.
Q27. For straight-line motion with uniform acceleration, what does the signed area under a velocity–time graph represent?
[UPSC CDS-I, 16 Apr 2023]
(A) Average velocity
(B) Net displacement
(C) Distance travelled in every case
(D) Average speed
Answer: (B) Net displacement
Explanation: Velocity multiplied by a short time interval gives displacement in that interval. Adding these contributions produces the signed area under the graph, equal to net displacement. Negative portions subtract from positive ones, so total distance need not equal the signed area.
Q26. A car initially moves at 12 m/s and is braked with a constant deceleration of 6 m/s². How far does it travel before stopping?
[UPSC CDS-I, 16 Apr 2023]
(A) 12 m
(B) 24 m
(C) 36 m
(D) 48 m
Answer: (A) 12 m
Explanation: Use the kinematic relation v² = u² + 2as. At rest v = 0, while u = 12 m/s and a = −6 m/s². Thus 0 = 144 − 12s, so the stopping distance is 12 metres.
Q25. A particle travels at speed v around a circle of radius r. What is the magnitude of its acceleration?
[WBCS Prelims, 2022]
(A) 0
(B) v/r
(C) v/r²
(D) v²/r
Answer: (D) v²/r
Explanation: Even when speed remains constant, the velocity vector changes direction around a circle. This requires centripetal acceleration towards the centre with magnitude v²/r. A zero acceleration would correspond to constant velocity in a straight line, not circular motion.
Q24. Consider two claims: I. Rolling friction is greater than sliding friction. II. Friction exerted by fluids is called drag. Which statement is correct?
[SSC MTS, 22 Jul 2022 (Shift 1)]
(A) Only I
(B) Neither I nor II
(C) Both I and II
(D) Only II
Answer: (D) Only II
Explanation: Rolling resistance is typically lower than sliding friction, so the first statement is incorrect. Air and water oppose relative movement of immersed objects through fluid resistance, commonly called drag. Thus the second statement is correct, and the correct choice is II only.
Q23. A heavy object and a light object possess equal kinetic energy. Which has greater linear momentum?
[WBCS Prelims, 2021]
(A) The heavier object
(B) The lighter object
(C) Both have the same momentum
(D) Both necessarily have zero momentum
Answer: (A) The heavier object
Explanation: Kinetic energy and momentum obey K = p²/(2m), which gives p = √(2mK). If kinetic energy is fixed, momentum magnitude grows as the square root of mass. Therefore the heavier body carries a greater momentum magnitude.
Q22. A person standing on a playground swing rises from a sitting position to standing. What happens to the period of oscillation?
[WBCS Prelims, 2021]
(A) It increases
(B) It stays unchanged
(C) It decreases
(D) It becomes zero
Answer: (C) It decreases
Explanation: Standing raises the combined centre of mass closer to the suspension point. This effectively shortens the pendulum length. Since the period varies as the square root of length, the period decreases, provided oscillations remain small enough for the pendulum approximation.
Q21. A uniform spring with force constant k is cut into two equal lengths. What is the force constant of each half?
[WBCS Prelims, 2021]
(A) k
(B) k/2
(C) 2k
(D) 4k
Answer: (C) 2k
Explanation: A uniform spring’s stiffness is inversely proportional to its length because shorter springs stretch less under the same force. Halving the original length therefore doubles the spring constant. Each half has stiffness 2k, even though the original complete spring had stiffness k.
