WAEC 2023 Physics · Question 2

When a light-weight body and a massive body are acted upon by the same force for the same period of time, the

Options

A.massive body has a higher momentum.
B.massive body builds up a higher velocity.
C.lighter body has a higher momentum.
D.momenta of both bodies remain the same.

Answer: D. momenta of both bodies remain the same.

Explanation written with AI and checked against the answer key

Analyze the question: The same force acts on two bodies of different masses for the same time. We are asked to compare momentum (and velocity).

Concept: Newton's second law in terms of momentum says force equals the rate of change of momentum:

F = Δp / Δt, so Impulse = F × t = Δp

Solution:

Both bodies feel the same force F for the same time t.
Impulse on each body = F × t, which is the same for both.
Both bodies start from rest, so the change in momentum equals the final momentum.
Therefore p₁ = p₂ = Ft. Their momenta are equal.

Checking the options:

A. Wrong. The massive body does not gain more momentum.
B. Wrong. Since p = mv, v = Ft/m, so the massive body gets the lower velocity.
C. Wrong. The lighter body has higher velocity, but not higher momentum.
D. Correct. The momenta gained are equal, since impulse is equal.

Tip: When you see "same force, same time," think impulse = Ft = change in momentum. Momentum gained is equal, while velocity gained depends on mass (v = Ft/m). Lighter bodies speed up more, but momentum stays equal.

AI can make mistakes. Report anything that looks wrong.