A stationary particle breaks into two parts of masses m_A and m_B which move with velocities v_A and v_B respectively. The ratio of their kinetic energies (K_B: K_A) is :

Solution

Physics sir · 3 steps

Both pieces carry the same momentum, so write each kinetic energy as 1/2pv and the ratio follows.

1. Momentum is conserved. The particle starts at rest, so the total momentum is zero before and after it breaks. The two parts fly apart with equal and opposite momenta, so m_A v_A = m_B v_B = p in magnitude.
2. Rewrite kinetic energy. Write K = 1/2mv² = 1/2(mv)v = 1/2pv. Both parts have the same p, so each kinetic energy depends only on its own speed.

   K_B/K_A = (1/2p v_B)/(1/2p v_A) = v_B/v_A = m_A/m_B

3. So. K_B : K_A = v_B : v_A, which is option (a). The lighter part moves faster and takes more of the kinetic energy.

The idea to keep. When a body at rest splits in two, the pieces share equal momentum. Then K = p²/2m, so kinetic energy goes inversely as mass and directly as speed.

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