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. 1
D. `m_(1)v_(2)/m_(2)v_(1)`

Answer

A

Explanation

`MV = m_(1)v_(1)-m_(2)v_(2)`
`0 = m_(1)v_(1)-m_(2)v_(2)`
`(m_(1))/(m_(2))=(v_(2))/(v_(1)) rArr (v_(1))/(v_(2)) =(m_(2))/(m_(1))`
`(E_(1))/(E_(2)) =(m_(1)v_(1)^(2))/(m_(2)v_(2)^(2))=m_(1)/(m_(2))((m_(2))/m_(1))^(2) =(m_(2))/(m_(1))`