JEE Main 2022 · 28 July · morning · Single correct · +4 / −1
In two different experiments, an object of mass 5 kg moving with a speed of 25 ms⁻¹ hits two different walls and comes to rest within (i) 3 second, (ii) 5 seconds, respectively. Choose the correct option out of the following :
- (a) Impulse and average force acting on the object will be same for both the cases.
- (b) Impulse will be same for both the cases but the average force will be different.
- (c) Average force will be same for both the cases but the impulse will be different.
- (d) Average force and impulse will be different for both the cases.
Answer and solution
Answer (b) Impulse will be same for both the cases but the average force will be different.
Solution
Physics sir · 2 steps
Impulse depends only on the change in momentum. The time only decides how hard the wall has to push.
- Impulse. Impulse equals the change in momentum. In both experiments the object goes from 25 m s⁻¹ to rest, so the change is the same: 0 - 5 × 25 = -125 N s.
F_(avg) = (Δ p)/(Δ t)
Case Stopping time Impulse (magnitude) Average force (i) 3 s 125 N s 125/3 ≈ 41.7 N (ii) 5 s 125 N s 125/5 = 25 N - So. The impulse is 125 N s in both cases, but the average force is different: it is larger when the object stops faster. The answer is (b).
The idea to keep. Same initial and final momentum means the same impulse, however long the collision lasts. A longer stopping time spreads that impulse out and gives a smaller average force. This is why airbags and cushions work.
Answer from the NTA final answer key. Solution by PrepWiser.