In the figure shown if mass of each block is m. Find the acceleration of block A.  
(use g=10 m/s²)

 

Let acc. of block A be a_A  and acc. of block B be a_B. Hence

$\begin{array}{l}2T=m{a}_A--\left(1\right)\\ and\\ mg-4T=m{a}_B---\left(2\right)\end{array}$

Constrained Motion : $\left(2T\right)a_A=\left(4T\right)a_B\left(\because T\propto \frac{1}{a}\right)$

$\Rightarrow a_A=2a_B$

After solving we get, 

$\begin{array}{l}from 2\times \left(1\right) and \left(2\right)\text{}\\ \Rightarrow 2\left( 2T=m{a}_A\right)\\ \Rightarrow 4T=2m{a}_A\text{} \\ \Rightarrow mg-4T=m\frac{a_A}{2}\text{}\\ on solving we get \text{}\\ \Rightarrow mg=\frac{ 5m{a}_A}{2}\\ \text{}\Rightarrow a_A=4m{s}^{-2}\end{array}$