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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

`"mu"^(2)`

B

`2/3"mu"^(2)`

C

`(mu"^(2))/4`

D

`("mu"^(2))/4`

Text Solution

Verified by Experts

The correct Answer is:
B
For the system `P_(i)=2"mu"hati+"mu"hatj`
As all the impulses are internal `vecP_(i)=vecP_(f)`
`vecP_(f)=3m vecu_(f)`, where `vecu_(f)` is the velocity of the combined mass after inelastic collision
Thus `3m vecu_(f)=2"mu"hatij," "vecu_(f)=(2u)/3hati+1/3hatjimplies|vecu_(f)|=sqrt(5/9)u`
Thus final energy of the system `=1/2xx3mxx|vecu_(f)|^(2)=1/2xx3mxx5/9u^(2)=(5"mu"^(2))/6`
Initial energy of the system `=(m_(1)v_(1)^(2))/2+(m_(2)v_(2)^(2))/2=1/2"mu"^(2)+1/2xx2mxxu^(2)=3/2"mu"^(2)`
Loss in K.E. `=[("Initial K.E.")-("Final K.E.")]`
Loss `=3/2"mu"^(2)-5/6"mu"^(2)=2/3"mu"^(2)`
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