Question

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 :

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

Answer 1

Answer: (B)

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

Answer 2

Let mass of one rod is $m$.
Balancing torque about hinge point.

$mg \left(C_{1}P\right) = mg \left(C_{2}N\right)$
$mg \left(\frac{L}{2} \sin\theta\right) = mg \left(\frac{L}{2} \cos\theta - L \sin\theta\right)$
$\Rightarrow \frac{3}{2} mg L \sin\theta = \frac{mgL}{2} \cos\theta$
$\Rightarrow \tan \theta = \frac{1}{3}$