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

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g/4

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g/2

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- g/2

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Solution

The correct option is B. g/4.
Consider the following diagram,

The acceleration of the whole system can be found by force balance i.e.,
$(3 m + m) a_{s y s} = 3 m g - m g$
$a_{s y s} = \frac{g}{2}$
So, $a_{c m} = \frac{m_{1} a + m_{2} a}{m_{1} + m_{2}} = \frac{m (\frac{g}{2}) + 3 m (- \frac{g}{2})}{m + 3 m}$
$a_{c m} = \frac{- g}{4}$
The negative sign shows that the acceleration is downwards.

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

The correct option is B. g/4.Consider the following diagram,The acceleration of the whole system can be found by force balance i.e.,(3m+m)asys=3mg−mgasys=g2So, acm=m1a+m2am1+m2=m(g2)+3m(−g2)m+3macm=−g4The negative sign shows that the acceleration is downwards.