In Fig. a pulley is shown which is frictionless and a ring of mass `m` can slide on the string without any friction. One end of the string is attached to point `B` and to the other end, a block `'P'` of mass `m` is attached. The whole system lies in vertical plane.
Now another block `'C'` of same mass `m` is attached to the block `'P'` and system is released from rest. If `a_(1)` and `a_(2)` are the magnitudes of initial accelerations of ring and blocks, respectively, then

Options

A. `a_(1)+a_(2)=g`
B. `a_(1)+2a_(2)=g`
C. `a_(1)=2a_(2)`
D. `2a_(1)=a_(2)`

Answer

B

Explanation

`2Tsintheta-mg=ma_(1),theta=30^(@)`
`2mg-T=2ma_(2)`
Simplify to get `a_(1)+2a_(2)=g`


From constraints we have initially
`a_(2)=2a_(1)sinthetaimpliesa_(2)=a_(1)`