Question

A wooden plank of length 1 m and uniform cross-section is hinged at one end to the bottom of a tank as shown. The tank is filled with water upto a height of 0.5 m. The specific gravity of the plank is 0.5. The angle $\theta$ made by the plank in equilibrium position is

• A. ${30}^o$
• B. ${45}^o$
• C. ${60}^o$
• D. ${90}^o$

Answer 1

The correct option is B ${45}^o$

Balancing torque abacus hinge

$\begin{array}{c}0.5\left(1.A\right)g\frac{1}{2}\sin \theta =\int \left(\frac{0.5A}{\cos \theta }\right)g\frac{0.5}{2\cos \theta }\sin \theta \\ \Rightarrow {\cos }^2\theta =\frac{1}{2}\\ \Rightarrow \cos \theta =\frac{1}{\sqrt{2}}\\ \Rightarrow \theta ={45}^0\end{array}$

$\therefore$ Option $B$ is correct.