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Two particles of same mass m moving with...

Two particles of same mass m moving with velocities `u_(1)` and `u_(2)` collide perfectly inelastically. The loss of energy would be :

A

`M/2 (u_2 -u_1)^2`

B

`M/2 (u_1 -u_2)^2`

C

`M/4 (u_1 -u_2)^2`

D

`M/4 (u_2 -u_1)^2`

Text Solution

Verified by Experts

The correct Answer is:
C
`M(u_1 +u_2) = 2Mv`
`implies v = ((u_1+u_2)/2)`
Loss of KE `=1/2 M(u_1^2+u_2^2)-1/2 2M((u_1+u_2)/2)^2`
`= M[(2u_1^2+2u_2^2+u_1^2-u_2^2-2u_1u_2)/4]`
`=M/4 (u_1 -u_2)^2`
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