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Question

Two particles having mass ratio n:1 are interconnected by a light inextensible string that passes over a smooth pulley. If the system is released, then the acceleration of the centre of mass of the system is :

A
(n1)2g
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B
(n+1n1)2g
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C
(n1n+1)2g
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D
(n+1n1)g
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Solution

The correct option is C (n1n+1)2g

Let mass of block A is m and the mass of block B is nm
nmgT=nma
Tmg=ma
Adding the above equations, we get
a=(n1)gn+1
Acceleration of the centre of mass of system.
aCOM=m1a1+m2a2m1+m2
aCOM=manma(n+1)m=anan+1=(n1n+1)2g
Here ve sign indicated that COM is moving downwards.

|aCOM|=(n1n+1)2g

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