As shown in the figure, two blocks of masses $4kg$ and $5kg$ are at rest on the ground. The masses are connected by a massless string passing over a smooth and light pulley. A $200N$ force is applied on the pulley. Find the difference in accelerations (in $m/s^2$ ) of the blocks.

Step1: Draw the free body diagram of the given problem.

Step2: Find the acceleration of the blocks $A$ and $B$.
From the $FBD$ of pulley,

$2T=200$
$\Rightarrow T=100N$
For block $A$,
$T-4g=4a_A$

$a_A=\frac{100-40}{4}=15m/s^2$

For block $B$,
$T-5g=5a_B$

$a_B=\frac{100-50}{5}=10m/s^2$

So, the difference in accelerations of the blocks
$\Rightarrow a_A-a_B=15-10=5m/s^2$

Final Answer:$5$