If kinetic energy of a body is increased by 300 % , then percentage change in momentum will be

Step-by-step solution

The kinetic energy K and momentum p of a body are related by the expression K = p^2 2m , where m is the mass of the body. Let the initial kinetic energy be K₁ and the initial momentum be p₁ . Then K₁ = p₁^2 2m . The kinetic energy is increased by 300 % , so the new kinetic energy K₂ is K₂ = K₁ + 300 % K₁ = K₁ + 3K₁ = 4K₁ . Let the new momentum be p₂ . Then K₂ = p₂^2 2m . Substituting K₂ = 4K₁ and K₁ = p₁^2 2m , we get p₂^2 2m = 4 p₁^2 2m , which simplifies to p₂^2 = 4p₁^2 , or p₂ = 2p₁ . The percentage change in mo