Question

A wooden plank of length $1\text{m}$ and uniform cross-section is hinged at one end to the bottom of the tank. The tank is filled with water upto a height of $0.5\text{m}$. The specific gravity of the plank is $0.5$. The plank makes an angle of ${45}^{\circ }$ with the vertical in the equilibrium position. $A$ is the midpoint of the plank. $B$ is the middle point of the dipped part of the plank. Which of the following are correct?

• A. The weight of the plank acts downwards at $A$
• B. The buoyant force acts through $B$
• C. $OB=\frac{1}{\sqrt{2}}\text{m}$
• D. Both (b) and (c)

Answer 1

Answer: (A), (B)

The buoyant force acts through $B$

Weight of the body acts through its COM, ie mid point of the plank$\left(A\right).$

Buouancy acts through COM of water displaced, ie midpoint of plank present in the water $\left(B\right)$

$l^{\prime }\cos {45}^{\circ }=h\Rightarrow l^{\prime }=\sqrt{2}h$

$\Rightarrow OB=\frac{l^{\prime }}{2}=\frac{h}{\sqrt{2}}=\frac{1}{2\sqrt{2}}$