Two bodies of mass 4 g and 25 g are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is :

Solution

Physics sir · 3 steps

Write momentum in terms of kinetic energy: with K fixed, p grows as the square root of mass.

1. Link p and K. Kinetic energy is K = p²/2m, so momentum can be written using K alone.

   p = √2mK

2. Take the ratio. Both bodies have the same K, so 2K cancels and p₁/p₂ = √(m₁/m₂) = √(4/25) = 2/5.
3. So. The momenta are in the ratio 2 : 5, option (c). The heavier body carries more momentum for the same kinetic energy.

The idea to keep. Whenever kinetic energies are equal, use p = √2mK: momentum goes as √m. The heavier body always has more momentum but less speed.

Answer from the NTA final answer key. Solution by PrepWiser.