Question

Two uniform rods of equal length but different masses are rigidly joined to form an $L$ shaped body, which is then smoothly pivoted about $O$ as shown. If the body is in equilibrium in the shown configuration, ratio $M:m$ will be :

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

Answer 1

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

Torque due to both the rods about pivot point O will be equal and opposite.
${\tau }_{mg}={\tau }_{Mg}$
$\therefore mg\times \frac{l}{2}\sin {60}^0=Mg\times \frac{l}{2}\sin {30}^0$
$mg\times \frac{l}{2}\times \frac{\sqrt{3}}{2}=Mg\times \frac{l}{2}\times \frac{1}{2}$
$\therefore \frac{M}{m}=\sqrt{3}$