The acceleration of the block `(A)` and `(B)` respectively in situation shown in the figure is: (pulleys and string are massless).

Options

A. `(2g)/(7)` downward, `(g)/(7)` upward
B. `(2g)/(3)` downward, `(g)/(3)` upward
C. `(10)/(13)g` downward, `(5g)/(13)` upward
D. none of these

Answer

A

Explanation

The F.B.D. of block `A` and `B` are
from constraint, the acceleration of `A` and `B` are `'2a'` and `'a'` respectively. Applying Newton's second law to block `A` and `B` , we get
`4g-T=4(2a)` (i)
`2T-5g=5(a)` (ii)
solving we get acceleration of `A` and `B` as `(2g)/(7)` .