Q. In the arrangement shown, the pulleys are smooth and the strings are inextensible. The acceleration of block $B$ is :

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A

$g / 5$

B

$5 g / 5$

C

$2 g / 5$

D

$2 g / 3$

Solution:

Let acceleration of $B$ is a downwards using $F B D$ of $A$ and $B$

$2 T-m g =\frac{m a}{2}\,\,\,...(1) $
$m g-T =m a $
$ \Rightarrow T =m g-m a\,\,\,...(2)$
From $(1)$ and $(2)$, we get
$ 2 m g-2 m a-m g =\frac{m a}{2}$
$m g =\frac{5 m a}{2} $
$ a =\frac{2 g}{5}$

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