A stationary partical explodes into two partical of a masses `m_(1) and m_(2)` which move in opposite direction with velocities `v_(1) and v_(2)`. The ratio of their kinetic energies `E_(1)//E_(2)` is

Options

A. `(m_(2))/(m_(1))`
B. `(m_(1))/(m_(2))`
C. `(2m_(2))/(m_(1))`
D. `(2m_(1))/(m_(2))`

Answer

A

Explanation

As stationary object explodes into masses `m_(1)` and `m_(2)` and move in opposite direction
According to conservation of momentum
`m_(1) v_(1) = - m_(2) v_(2) implies (v_(1))/(v_(2)) = (- m_(2))/(m_(1))`
Now , ratio of KE
`(KE_(1))/(KE_(2)) = (1//2 m_(1) v_(1)^(2))/(1//2 m_(2) v_(2)^(2)) = (m_(1))/(m_(2)) [ (m_(2))/(m_(1))]^(2) = (m_(2))/(m_(1))`