Question

A light and heavy object have the same momentum. Find out the ratio of their Kinetic Energies. Which one has a larger Kinetic Energy.

Answer 1

Let the mass of the lighter object be m₁ and of the heavier one be m₂, velocities be v₁ and v₂ and momentum be p.

Since their momentum is the same, p = m₁v₁ = m₂v₂.

Since, m₁ < m₂, v₁ > v₂.

Now, Kinetic Energy of object with mass m₁, EK₁ = (1/2)(m₁)(v₁)².

Kinetic energy of object with mass m₂, EK₂ = (1/2)(m₂)(v₂)².

EK₁ : EK₂ = (1/2)(m₁)(v₁)² ÷ (1/2)(m₂)(v₂)² = (m₁.v₁²)/(m₂.v₂²)

On comparing, EK₁ = m₁.v₁² and EK₂ = m₂.v₂²

Since, m₁ < m₂ and v₁ > v₂

EK₁ will be more than EK₂.