Two particles having masses 4 g and 16 g respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is n : 2. The value of n will be ___________.

Solution

Physics sir · 3 steps

Equal kinetic energy means momentum goes as the square root of mass, so the lighter one has less.

1. Link p and K. Kinetic energy is K = p²/2m, so momentum is p = √2mK.

   p₁/p₂ = √(m₁/m₂) (K₁ = K₂)

2. Put in numbers. With m₁ = 4 g and m₂ = 16 g, p₁/p₂ = √(4/16) = 1/2.
3. So. The ratio is 1 : 2. Matching it with n : 2 gives n = 1.

The common slip: 4. Writing p ∝ 1/√m flips the ratio to 2 : 1, which gives n = 4. Speed goes as 1/√m, but momentum goes as √m.

The idea to keep. Whenever kinetic energies are equal, use p = √2mK. Momentum grows as √m, so the heavier body carries more momentum even though it moves slower.

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