Question

The acceleration of block A is $a$ upwards and the acceleration of block C is $f$ downwards. Find the acceleration of block B. Assume that the string is inextensible and all the pulleys are smooth and light.

• A. $\frac{1}{2}(f-a)$, Upwards
• B. $\frac{1}{2}(a+f)$, Downwards
• C. $\frac{1}{2}(a+f)$, Upwards
• D. $\frac{1}{2}(f-a)$, Downwards

Answer 1

The correct option is A $\frac{1}{2}(f-a)$, Upwards



$l_A$, $l_B$ and $l_C$ are the intercepts of the same string.
Since the string is inextensible,
$l_A+2l_B+l_C$ = constant
Double differentiating above equation w.r.t time $t$, we get equation in terms of acceleration,
$-a_A-2a_B+a_C=0$
(Assuming increase in length as positive)
Since $a_A=a,a_C=f$
$\Rightarrow a_B=\frac{f-a}{2}$ (Upwards)