When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be :

Solution

Physics sir · 3 steps

Momentum goes as the square root of kinetic energy, so 36 times the KE means only 6 times the momentum.

1. Link p and K. With K = 1/2mv² and p = mv, you get K = p²/2m. For the same body the mass is fixed, so p is proportional to √K.

   p₂/p₁ = √(K₂/K₁) = √36 = 6

2. Find the increase. The new momentum is 6p₁, so the increase is 6p₁ - p₁ = 5p₁. As a percentage of the original, that is 5p₁/p₁ × 100 = 500%.
3. So. The momentum increases by 500%, which is option (b).

The idea to keep. For a fixed mass, p = √2mK. And percentage increase is (new minus old) over old: becoming 6 times means a 500% increase, not 600%.

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