In the arrangement shown, the pulleys are smooth and the strings are inextensible. Find the acceleration of block B in m/s². Take g=10 m/s² 

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

$\begin{array}{l}2T-mg=\frac{ma}{2}\\ mg-T=ma\\ \Rightarrow T=mg-ma\end{array}$

From (i) and (ii), we get

$\begin{array}{l}2mg-2ma-mg=\frac{ma}{2}\\ mg=\frac{5ma}{2}\Rightarrow a=\frac{2g}{5}=4.00\mathrm{m}/{\mathrm{s}}^2\end{array}$