Question

Two bodies of different masses are acted upon by the same force for the same time. They will acquire the same:

• A. Velocity
• B. Kinetic energy
• C. Acceleration
• D. Momentum

Hint:

Impulse equals force times time, and impulse always equals the change in momentum.

Answer 1

The Correct Option is D

Step 1: Newton's second law states that force equals the rate of change of momentum, so \(F = \dfrac{\Delta p}{\Delta t}\), which rearranges to \(\Delta p = F \times \Delta t\). The quantity \(F \times \Delta t\) is called impulse.

Step 2: Both bodies experience the same force \(F\) for the same time \(\Delta t\), so the impulse delivered to each body is identical.

Step 3: Since impulse equals the change in momentum, and both bodies receive the same impulse, both bodies gain exactly the same amount of momentum, no matter how different their masses are.

Step 4: Velocity is not the same, because \(v = p/m\), and the masses differ. Acceleration is not the same, because \(a = F/m\), and a smaller mass gets a larger acceleration for the same force. Kinetic energy is not the same either, because \(KE = p^2/(2m)\), so a smaller mass with the same momentum has more kinetic energy.

Answer: Momentum, option D.