KVPY SA Exam 2016 Question Paper

For one arm to remain horizontal the net torque about O must be zero (in the position shown in the figure)
for this OP = OQ
$\Rightarrow \mathit{O}\mathit{Q}=\frac{\mathit{l}}{2}\cos \mathit{\theta }$
from figure
AE = AC + CE
$\Rightarrow \mathrm{AE}=\mathit{l}\cos \mathit{\theta }+\mathit{O}\mathit{Q}$
$\Rightarrow \frac{\mathit{l}}{2}=\mathit{l}\cos \mathit{\theta }+\frac{\mathit{l}}{2}\cos \mathit{\theta }$
$\Rightarrow \cos \mathit{\theta }=\frac{1}{3}$
hence $\mathit{\theta }={\cos }^{\mathit{–}1}\left(\frac{1}{3}\right)$
correct Answer is (A)