Question

In the given figure a ring of mass $m$ is kept on a horizontal surface while a body of equal mass m is attached through a string, which is wounded on
the ring, When the system is released, the ring rolls without slipping Consider the following statement and choose the correct option
(i) acceleration of the centre of mass of ring is $\frac{2g}{3}$
(ii) acceleration of hanging particle is $\frac{4g}{3}$
(iii) frictional force (on the ring) acts in forward direction
(iv) frictional force (on the ring) acts in backward direction

• A. statement (i) and (ii) only are correct
• B. statement (ii) and (iii) only are correct
• C. statement (iii) and (iv) only are correct
• D. None of these

Answer 1

The correct option is D None of these

For Block
$mg-T=m\left(2a\right)....\left(i\right)$
For Ring $T+f=ma...\left(ii\right)$
$\frac{(T-f)R}{m{R}^2}=\alpha ...\left(iii\right)$
$a=R\alpha .....\left(iv\right)$
Solving these equations we get
$a=\frac{g}{3},2a=\frac{2g}{3},T=\frac{mg}{3}$ and $f=0$