Three bodies A, B and C have equal kinetic energies and their masses are 400 g, 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is :

Solution

Physics sir · 4 steps

Same kinetic energy means momentum goes as the square root of mass, so just compare the masses.

1. Link p and K. Kinetic energy is K = p²/2m. Rearranging gives the momentum in terms of mass and kinetic energy.

   p = √2mK ⇒ p ∝ √m when K is the same

2. Same units first. Convert 400 g to 0.4 kg. The masses are then 0.4 : 1.2 : 1.6, which divides down to 1 : 3 : 4.
3. Take square roots. p_A : p_B : p_C = √1 : √3 : √4 = 1 : √3 : 2.
4. So. The ratio of their linear momenta is 1 : √3 : 2, option (a).

The idea to keep. Remember p = √2mK. Equal kinetic energy means p ∝ √m, so the heavier body always carries more momentum. Bring all masses to the same unit first.

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