A particle of mass m1 is moving with a velocity `v_(1)` and another particle of mass `m_(2)` is moving with a velocity v2. Both of them have the same momentum but their different kinetic energies are E1 and E2 respectively. If `m_(1) gt m_(2)` then

Options

A. `(E_(1))/(E_(2)) = (m_(1))/(m_(2))`
B. `E_(1) gt E_(2)`
C. `E_(1) =E_(2)`
D. `E_(1) lt E_(2)`

Answer

D

Explanation

`m_(1)v_(1)=m_(2)v_(2)rArr (v_(1))/(v_(2)) = (m_(2))/(m_(1))`
`(E_(1))/(E_(2)) = (1/2m_(1)v_(1)^(2))/(1/2m_(2)v_(2)^(2)) = (m_(1))/(m_(2)) ((m_(2))/(m_(1)))^(2)`
`(E_(1))/(E_(2)) = (m_(2))/(m_(1))`
Given `m_(1) gt m_(2)`
`(E_(1))/(E_(2)) lt 1 " " rArr E_(1) lt E_(2)`