Question

For the system shown below, block $B$ is moving upward with an acceleration $a$. What will be the acceleration of block $A$, if the string is inextensible and pulleys are frictionless?

• A. $a$
• B. $2a$
• C. $4a$
• D. $a/2$

Answer 1

The correct option is B $2a$

If $B$ is moving upwards, the movable pulley connected to $B$ also moves with the same acceleration upwards.

Since the string is inextensible, the length of the string remain same. If $l_1$, $l_2$ and $l_3$ are intercepts of the string,
$l_1+l_2+l_3=\text{constant}$
Differentiating twice w.r.t time $t$, we get
$\frac{d^2{l}_1}{d{t}^2}+\frac{d^2{l}_2}{d{t}^2}+\frac{d^2{l}_3}{d{t}^2}=0$
Taking downward acceleration to be positive and upward negative.
$\Rightarrow a_A-a_B-a_B=0\Rightarrow a_A=2a_B$
$\Rightarrow a_A=2a$