Question

Two uniform rods of equal length but different masses are rigidly joined to form an $L$ - shaped body which is pivoted about point $\text{O}$ as shown. If in the shown configuration, the body is in equillibrium, the ratio $M/m$ will be.

• A. $2$
• B. $\sqrt{3}$
• C. $\sqrt{2}$
• D. $\frac{1}{\sqrt{3}}$

Answer 1

The correct option is B $\sqrt{3}$

In equilibrium, torque of forces $mg$ and $Mg$ about an axis passing through $\text{O}$ balance each other.
$Mg\frac{L}{2}\sin {30}^{\circ }=mg\frac{L}{2}\sin {60}^{\circ }$
$\Rightarrow \frac{M}{m}=\sqrt{3}$