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A circular ring of mass M and radius 'a'...

A circular ring of mass `M` and radius `'a'` is placed in a gravity free space. A small particle of mass `m` placed on the axis of the ring at a distance `sqrt(3)a` from the center of the ring, is released from rest. The velocity with which the particle passes through the center of the ring is

A

`sqrt((GM)/(a))`

B

`sqrt((GM)/(2a)((m)/(M)))`

C

`sqrt((GM)/(2a)((M)/(m)))`

D

`sqrt((GM)/(a)((M)/(M+m)))`

Text Solution

Verified by Experts

From `COM`, `mv_(1)-Mv_(2)=0` ………….`(1)`
From `COE`, `-(GMm)/(2a)=-(GMm)/(a)+(1)/(2)mv_(1)^(2)+(1)/(2)Mv_(2)^(2)` ………`(2)`
From Eqs. `(1)` and `(2)`,
`v_(1)=sqrt((GM)/(a)((M)/(m+M)))`
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