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Two particles of mass m & 2m have veloci...

Two particles of mass m & 2m have velocities `u hat( j) ` & `u hat( i ) ` respectively . They collide completely inelastically. Find the loss in kinetic energy of the system.

A

`(3)/(4) m u^(2)`

B

`sqrt((2)/(3)) m u^(2)`

C

`(1)/(3) m u^(2)`

D

`(1)/(8) m u^(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Conserving momentum- `m u hat(i) + m ((u)/(2) hat(i) + (u)/(2) hat(j))= 2m (v_(1) hat(i) + v_(2) hat(j))`
`v_(1)= (3u)/(4) and v_(2)= (u)/(4)`
Energy loss= Change in K.E
`= [(1)/(2) m u^(2) + (1)/(2) m ((u)/(2) sqrt2)^(2)]- [(1)/(2) (2m) ((9u^(2))/(16)+ (u^(2))/(16))]`
`= (3 m u^(2))/(4)- (5 m u^(2))/(8)= (m u^(2))/(8)`
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