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)upsilon_(2)//m_(2)upsilon_(1)`

Answer

A

Explanation

According to the principlce of conservation of linear momentum,
`m_(1)upsilon_(1)-m_(2)upsilon_(2):. (m_(1))/(m_(2))=(upsilon_(2))/(upsilon_(1))`
`(E_(1))/(E_(2))=((1)/(2)m_(1)upsilon_(1)^(2))/((1)/(2) m_(2)upsilon_(2)^(2))=(m_(1))/(m_(2))((upsilon_(1))/(upsilon_(2)))^(2)=(m_(1))/(m_(2))((m_(2))/(m_(1)))^(2)`
`(E_(1))/(E_(2))=(m_(2))/(m_(1))`