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A uniform stick AB of mass M is tied to one of a light inextensible string OA. A horizontal force $F = m g$ is applied at end B of the stick and it remains in equilibrium in the position shown. If $α = \tan^{- 1} (n),$ the value of $n$ is

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answer is 2.

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Detailed Solution

For translational equilibrium $T \cos β = M g a n d T \sin β = F = M g \Rightarrow β = 45^{\circ}, T = \sqrt{2} M g .$

For translational equilibrium net torque about any point =0

$i . e a b o u t C, F \frac{l}{2} \cos α + T \sin β \frac{l}{2} \cos α - T \cos β \frac{l}{2} \sin α = 0$

$∴ M g \cos α + M g \cos α = M g \sin α \Rightarrow 2 \cos α = \sin α \Rightarrow \tan α = 2$

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