If the Kinetic energy of a moving body becomes four times its initial Kinetic energy, then the percentage change in its momentum will be :

Solution

Physics sir · 3 steps

Momentum goes as the square root of kinetic energy, so 4 times the KE means only 2 times the momentum.

1. Link KE and momentum. With p = mv and K = 1/2mv², you get K = p²/2m. The mass does not change, so p is proportional to √K.

   p = √2mK ⇒ p₂/p₁ = √(K₂/K₁) = √4 = 2

2. Percentage change. The momentum becomes 2p₁, so the change is 2p₁ - p₁ = p₁. As a percentage, p₁/p₁ × 100 = 100%.
3. So. The momentum increases by 100%, which is option (a).

The idea to keep. For a fixed mass, p = √2mK. Take the square root of the KE ratio to get the momentum ratio, then subtract 1 for the percentage change.

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