A uniform rod of mass M and length L is place | vedclass

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Question

(B) According to the law of conservation of linear momentum,the total momentum of the system before the collision must equal the total momentum after

Vedclass · Accepted Answer

$mv/M$

Vedclass · Answer

(B) According to the law of conservation of linear momentum,the total momentum of the system before the collision must equal the total momentum after the collision.Before the collision,the momentum of the system is $P_i = mv + M(0) = mv$.After the collision,the particle comes to rest,so its momentum is $0$. Let the velocity of the centre of mass of the rod be $V_{cm}$. The momentum of the rod is $M V_{cm}$.Thus,$P_f = 0 + M V_{cm} = M V_{cm}$.Equating initial and final momentum: $mv = M V_{cm}$.Solving for $V_{cm}$,we get $V_{cm} = \frac{mv}{M}$.

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