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A particle of mass m is rigidly attached...

A particle of mass `m` is rigidly attached at `A` to a ring of mass `3m` and radius `r`. The system is released from rest and rolls without sliding. The angular acceleration of ring just after release is

A

`g/(4r)`

B

`g/(6r)`

C

`g/(8r)`

D

`g/(2r)`

Text Solution

Verified by Experts

The correct Answer is:
B
The distance of CM from the ring centre O. `x=(3m(0) + m( r))/(3m+m) = r/4`
We can apply torque about point of contact as the ring is rolling, `tau p = I_(p) alpha`
`4mg(r/4) = [(3mr^(2) + mr^(2))+m(AP)^(2)]_(alpha) rArr mgr = [4mr^(2) + m(sqrt(2)r)^(2)]alpha rArr mgr = 6mr^(2) alpha rArr g/(6r)`
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