Work, Energy and Power — Question 12

Given,

Velocity of first body v₁ = v

Velocity of second body, v₂ = 2v

As the mass of the two bodies are same and as kinetic energy is directly proportional to the square of the velocity (K α v²)

Hence, ratio of their kinetic energies is

$\dfrac{K_1}{K_2} = \dfrac{(v_1)^2}{(v_2)^2} \\[0.5em] \dfrac{K_1}{K_2} = \dfrac{v^2}{(2v)^2} \\[0.5em] \dfrac{K_1}{K_2} = \dfrac{v^2}{4v^2} \\[0.5em] \dfrac{K_1}{K_2} = \dfrac{1}{4} \\[0.5em]$