Question

The acceleration of the blocks (A) and (B) respectively in situation shown in the figure is: (pulleys and strings are massless)

• A. $\frac{2g}{7}$ downward, $\frac{g}{7}$ upward
• B. $\frac{2g}{3}$ downward, $\frac{g}{3}$ upward
• C. $\frac{10}{13}\,g$ downward , $\frac{5 g}{13}$ upward
• D. none of these

Answer 1

Answer: (A)

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 blocks A and B, we get
$4g-T=4(2a) \ldots(i)$
$2T-5g=5 (a) \ldots(ii)$
Solving we get acceleration of A and B as $\frac{2g}{7}$