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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 :

(1) $\tan\theta={2\over\sqrt{3}}$

(2) $\tan\theta={1\over3}$

(3) $\tan\theta={1\over2}$

(4) $\tan\theta={1\over2\sqrt{3}}$

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Ans: (2) $\tan\theta = {1\over3}$

Sol:

 

Let mass of one rod is m. 

Balancing torque about hinge point. 

mg (C1P) = mg (C2N) 

$mg\left({L\over2}\sin\theta\right)= mg({L\over2}\cos\theta - L\sin\theta)$

$\implies{3\over2}mgL\sin\theta= {mgL\over2}\cos\theta$

$\implies\tan\theta = {1\over3}$

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