An L- shaped object, made of thin rods of uniform mass density, is suspended with a string as shown

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6.System of Particles and Rotational Motion

hard

An $L-$ shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If $AB = BC$, and the angle made by $AB$ with downward vertical is $\theta$ then

$\tan \,\theta = \frac{1}{{2\sqrt 3 }}$

$\tan \,\theta = \frac{1}{3}$

$\tan \,\theta = \frac{2}{{\sqrt 3 }}$

$\tan \,\theta = \frac{1}{2}$

(JEE MAIN-2019)

Solution

Lets considered mass of each rod is m for stable equilibrium the torque about point $O$ should be zero. Torque balance about $O$

$\begin{array}{l}
mg\frac{a}{2}\sin \theta = mg\left( {\frac{a}{2}\cos \theta – a\sin \theta } \right)\\
\tan \theta = \frac{1}{3}\\
\Rightarrow {\tan ^{ – 1}}\left( {\frac{1}{3}} \right)
\end{array}$

Standard 11

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