Two solids A and B of mass 1 kg and 2 kg respectively are moving with equal linear momentum. The ratio of their kinetic energies (K.E.) A : (K.E.) B will be A/1, so the value of A will be ________.

Solution

Physics sir · 3 steps

Same momentum for both, so write KE in terms of p and the lighter body carries more energy.

1. KE from momentum. With p = mv, you get v = p/m. Put this into 1/2mv² to write kinetic energy using momentum alone.

   K = p²/2m

2. Take the ratio. Both bodies have the same p, so p² and the 2 cancel. That leaves K_A/K_B = m_B/m_A = (2 kg)/(1 kg) = 2/1.
3. So. K_A : K_B = 2 : 1, so A = 2.

The common slip: 0.5. Taking K as directly proportional to mass gives K_A : K_B = 1 : 2, which is 0.5. At fixed momentum the ratio is inverse.

The idea to keep. At equal momentum, K = p²/2m makes kinetic energy inversely proportional to mass. The lighter body moves faster and carries more energy.

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