Question

Find the value of $M$ in terms of m if the system is in equilibrium.

• A. $2m$
• B. $m$
• C. $\frac{m}{2}$
• D. $\frac{m}{3}$

Answer 1

The correct option is B $m$

FBDs of the body $B$, middle pulley and body $A$ is as shown.

From the condition of equilibrium, we have
$T^{\prime }=mg$ and $T^{\prime }=2T$
$⟹T=\frac{mg}{2}$......(i)
And, $2T=Mg$
Using (i), we get
$⟹2\times \frac{mg}{2}=Mg$
$\Rightarrow M=m$