Question

An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as showm=n in figure. If $AB=BC$, and the angle made by $AB=B$, 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)

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

Let the mass of one of is $m$.

Balancing torque about the point

$mg\left(C_{1}P\right)=mg\left(C_{2}N\right)$

$mg\left(\frac{L}{2}\sin \theta \right)=mg(\frac{L}{2}\cos \theta -L\sin \theta )$

$\Rightarrow \frac{3}{2}mgL\sin \theta =\frac{mgL}{2}\cos \theta$

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