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

Options

A. `1:1`
B. `2:1`
C. `4:1`
D. `9:1`

Answer

D

Explanation

K.E. of colliding body before collision `= (1)/(2) m v^(2)`
After collision its velocity becomes
`v. = ((m_(1) - m_(2)))/((m_(1) + m_(2))) v = (m)/(3m) v = (v)/(3)`
`therefore` K.E. after collision `(1)/(2)m v^(2) = (1)/(2) (mv^(2))/(9)`
Ratio of kinetic energy `= (K.E._("before"))/(K.E._("after")) = ((1)/(2)m v^(2))/((1)/(2)(mv^(2))/(9)) = 9 :1`