Question

In the arrangement shown, neglect the mass of the ropes and the pulley. What must be the value of $m$ to keep the system in equilibrium? (Neglect friction every where).

• A. $M$
• B. $2M$
• C. $\frac{M}{2}$
• D. $\frac{M}{4}$

Answer 1

The correct option is C $\frac{M}{2}$

For equilibrium;

$T_1=mg\sin {30}^{\circ }=\frac{Mg}{2}$

So from figure at the lower pulley ;

$2T_1=2mg\Rightarrow T_1=mg$

$\Rightarrow =mg\Rightarrow m=\frac{M}{2}$

So (C) is correct.