A body of mass m moving with velocity v makes a head-on collision with another body of mass 2 m which is initially at rest. The loss of kinetic energy of the colliding body (mass m ) is

Options

A. `(1)/(2)` of its initial kinetic energy
B. `(1)/(9)` of its initial kinetic energy
C. `(8)/(9)` of its initial kinetic energy
D. `(1)/(4)` of its initial kinetic energy

Answer

C

Explanation

`(Delta K)/(K)= [1- ((m_(1)-m_(2))/(m_(1) + m_(2)))^(2)] = [1- ((m-2m)/(m+2m))^(2)] = (8)/(9)`
`Delta K= (8)/(9)K` i.e. loss of kinetic energy of the colliding body is `(8)/(9)` of its initial kinetic energy