A stick of square cross-section (5 cm×5 cm) and length ‘4 m’ weighs 2.5 kg is in equilibrium as shown in the figure below. Determine its angle of inclination (in degree) in equilibrium when the water surface is 1 m above the hinge.

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A stick of square cross-section $(5 c m \times 5 c m)$ and length ‘4 m’ weighs 2.5 kg is in equilibrium as shown in the figure below. Determine its angle of inclination (in degree) in equilibrium when the water surface is 1 m above the hinge.

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answer is 30.

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Detailed Solution

   $O E = l$
   $l = \frac{1}{\sin θ} ........... (i)$
$O D = 2 \cos θ ............ (i i)$
$O C = \frac{l}{2} \cos θ = \frac{\cos θ}{2 \sin θ} .......... (i i i)$
$F_{B} = ρ_{w} A l g$
Torque about $O$
   $m g (O D) = ρ_{w} A l g (O C)$
On solving
   $\sin^{2} θ = \frac{1}{4}$
   $θ = 30^{0}$