Physics - NLM Question with Solution | TestHub

Let $T$ be the tension in the string and $a$ be the acceleration of the system.

The heavier mass $\frac{3}{2}m$ moves downwards and the lighter mass $m$ moves upwards.

Writing the equations of motion for both masses:

For mass $m$ (moving upwards):
$T-mg=ma$

For mass $\frac{3}{2}m$ (moving downwards):
$\frac{3}{2}mg-T=\frac{3}{2}ma$

Adding the two equations, we get:
$\frac{3}{2}mg-mg=ma+\frac{3}{2}ma$

$\frac{1}{2}mg=\frac{5}{2}ma$

$a=\frac{g}{5}$

Therefore, the mass $m$ will ascend with an acceleration of $\frac{g}{5}$.

Answer: $\frac{g}{5}$