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

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

Laws of Motion

Solution:

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