Two bodies A and B of masses 5 kg and 8 kg are moving such that the momentum of body B is twice that of the body A. The ratio of their kinetic energies will be :

Solution

Physics sir · 3 steps

Momenta are given, so write kinetic energy in terms of momentum: K = p²/2m.

1. KE from momentum. Since p = mv, you can write 1/2mv² as p²/2m. This form uses exactly what the question gives you: masses and momenta.

   K_A/K_B = (p_A²/2m_A)/(p_B²/2m_B) = (p_A/p_B)² × m_B/m_A

2. Put in numbers. p_B = 2p_A, so p_A/p_B = 1/2 and its square is 1/4. The mass ratio is m_B/m_A = 8/5. Then K_A/K_B = 1/4 × 8/5 = 2/5.
3. So. The ratio of kinetic energies K_A : K_B is 2 : 5, which is option (b).

The idea to keep. Whenever momenta are compared, use K = p²/2m. Kinetic energy goes as the square of momentum and inversely as mass, so square the momentum ratio first.

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