NDA 2026 · PYQ · Mechanics / Reference Frames and Kinetic Energy · hard
A ball is dropped from rest from height h above the ground in frame S (the Earth's frame). Another frame S' is moving upwards with constant speed u relative to the Earth. In frame S', the ball has initial downward speed v. Pertaining to the change in kinetic energy (ΔK) of the ball from release to just before hitting the ground as measured in frames S and S' separately, which one of the following is correct?
A.ΔK is the same in both the frames.
B.ΔK is larger in frame S.
C.ΔK is larger in frame S'.✓ Correct
D.ΔK cannot be compared without the information of mass of the ball.
Explanation
In frame S, initial speed is 0 and final speed is √(2gh), so ΔK_S = (1/2)m(2gh) = mgh. In frame S' (moving up with speed u), initial downward speed of ball is v = u, and final downward speed = √(2gh) + u. Thus ΔK_S' = (1/2)m[(√(2gh)+u)² - u²] = (1/2)m[2gh + 2u√(2gh)] = mgh + mu√(2gh). Since the additional term mu√(2gh) is positive, ΔK is larger in frame S'. Kinetic energy is not Galilean-invariant; its change differs across frames moving relative to each other.
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