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.

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

Answer 1

The correct option is A $2m$

FBDs of the bodies $A,B$ and the movable pulley are as shown.

From the equilibrium condition, we have
$T=mg$
And, $T^{{}^{\prime }}=2T$
And, $T^{{}^{\prime }}=m_B.g=2T$
$\Rightarrow T=\frac{m_B.g}{2}$
$\Rightarrow 2mg=m_{B}g⟹m_B=2m$