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Pulley

If the mass o...

Question

If the mass of the body $A$ is $m$ . Find the mass of the body $B$ in terms of mass of the body $A$ for the system to be in equilibrium.

2 m

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\frac{m}{2}

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3 m

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\frac{m}{3}

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Solution

The correct option is A $2 m$
FBDs of the bodies $A, B$ and the movable pulley are as shown.

From the equilibrium condition, we have
$T = m g$
And, $T^{^{'}} = 2 T$
And, $T^{^{'}} = m_{B} . g = 2 T$
$\Rightarrow T = \frac{m_{B} . g}{2}$
$\Rightarrow 2 m g = m_{B} g ⟹ m_{B} = 2 m$

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