A bullet of mass 50 g is fired with a speed 100 m / s on a plywood and emerges with 40 m / s. The percentage loss of kinetic energy is :

Solution

Physics sir · 4 steps

Kinetic energy goes as v², so square the speed ratio first; the mass never enters the answer.

1. Ratio of energies. Both kinetic energies use the same mass m, so 1/2m cancels when you take the ratio. Only the ratio of the speeds, squared, survives.

   K_f/Kᵢ = (v_f/vᵢ)² = (40/100)² = 0.16

2. Fraction lost. The bullet keeps 16% of its kinetic energy. The fraction lost is 1 - 0.16 = 0.84.
3. Check with numbers. With m = 0.05 kg: Kᵢ = 1/2 × 0.05 × 100² = 250 J and K_f = 1/2 × 0.05 × 40² = 40 J. The loss is 210 J, and 210/250 = 0.84.
4. So. The percentage loss of kinetic energy is 84%, option (c).

The idea to keep. For a percentage change in kinetic energy at fixed mass, work only with v². Ask whether the question wants what remains or what is lost.

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