JEE Main 2022 · 26 July · evening · Single correct · +4 / −1
A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momentum will be :
- (a) 1 : 1
- (b) 2 : 1
- (c) 1 : 4
- (d) 4 : 1
Answer and solution
Answer (b) 2 : 1
Solution
Physics sir · 3 steps
Link momentum to kinetic energy with p = √2mK; with equal K, momentum goes as the square root of mass.
- Connect p and K. Kinetic energy is K = p²/2m, because p = mv. Rearranging gives momentum in terms of kinetic energy.
p = √2mK
- Take the ratio. Both bodies have the same K, so it cancels: p₁/p₂ = √(m₁/m₂) = √(8/2) = √4 = 2.
- So. The momenta are in the ratio 2 : 1, option (b). The heavier body moves slower but still carries more momentum.
The idea to keep. Whenever kinetic energy is fixed, use p = √2mK. Momentum then scales as √m, not as m.
Answer from the NTA final answer key. Solution by PrepWiser.