Two bodies of different masses m₁ and m₂ have equal momenta. Their kinetic energies E₁ and E₂ are in the ratio

Step-by-step solution

Given - Momentum of two bodies are same i.e. p₁=p₂ and mass of two bodies m₁ and m₂ The relationship between the kinetic energy (KE) and Linear momentum ( p ) is - Momentum of first body whose mass is m ₁ . p= 2 m₁ K E₁ ... (1) Momentum of second body whose mass is m ₂p= 2 m₂ K E₂ ... (2) Divide equation (1) and (2). aligned & p p = 2 m₁ K E₁ 2 m₂ K E₂ & 2 m₂ K E₂ = 2 m₁ K E₁ aligned By squaring both side, we get aligned & 2 m₂ K E₂=2 m₁ K E₁ & K E₁ K E₂ = m₂ m₁ aligned