Question

The accelerations of the blocks A and B respectively as seen in the situation shown in the figure are (pulleys & strings are massless and pulleys are frictionless, acceleration due to gravity is $g$)

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

Answer 1

Answer: (A)

$\frac{2g}{7}$downward, $\frac{g}{7}$ upward

We can see that two segments of string holding the mass 5kg is balanced by a string carrying mass $4$$kg$.

If acceleration is a on $5$ $kg$ side, it is $2$$a$ on $4$ $kg$ side (Pulley constraint problem)
Let us consider the movement of 4kg mass to be downward. Therefore.
$4g-T=4\left(2a\right)........\left(i\right)$
On the other side, we have
$2T-5g=5\left(a\right)........\left(ii\right)$
Solving i and ii, we have
Acceleration of block $A=\frac{2g}{7}$ downwards
and acceleration of block $B=\frac{g}{7}$ upwards
Answer is A