in the given figure a ring of mass `m` is kept on a horizontal surface while a body of equal mass `m` si attached through 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 options.
(i). Acceleration of centre of mass of ring is `(2g)/(3)`
(ii). acceleration of hanging particle is `(4g)/(3)`
(iii). Frictional force (on the ring) acts in backward direction.
(iv) . Frictional force (on the ring) acts in backward direction.

Options

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

Explanation

`mg-T=m(2a)` ..(i)
For ring
`T+f=ma` …(ii)
`((T-f)R)/(mR^(2))=alpha` ..(iii)
`a=Ralpha` .(iv)
Solving these equation we get
`a=(g)/(3),2a=(2g)/(3),T=(mg)/(3)` and `f=0`