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  4. A pulley fixed with ceiling carries a string with blocks of mass m and 3m attached to its ends. The masses of string and pulley are negligible. When the system is released, its centre of mass moves with acceleration

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Q. A pulley fixed with ceiling carries a string with blocks of mass $m$ and $3m$ attached to its ends. The masses of string and pulley are negligible. When the system is released, its centre of mass moves with acceleration

NTA AbhyasNTA Abhyas 2020Laws of Motion

Solution:

The magnitude of the acceleration of each mass with respect to the pulley
$a=\frac{3 m g - m g}{\left(3 m + m\right)}=\frac{g}{2}$
Solution
Acceleration of centre of mass $=\frac{\left(3 m\right) \, g / 2 - m g / 2}{\left(3 m + m\right)}=\frac{g}{4}$