Question

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. `v/(8r)`
D. `g/(2r)`

Answer 1

Correct Answer - B
The distance of `CM` from the ring centre `O`
`x+(3m(0)+m(r))/(3m+m)=r/4`
We can apply torque equation about point of contact at the ring is rolling.
`tau_(P)=I_(P)alpha`
`4mg(r/4)=[(3mr^(2)+mr^(2))m(AP)^(2)]alpha` ltbr gt `implies mgr=[4mr^(2)+m(sqrt(2)r)^(2)]alpha`
`implies mgr=6mr^(2)alphaimplies g/(6r)`