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A wooden plank of length 1 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 m. The specific gravity of the plank is 0.5. The plank makes an angle of 45 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
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B
The buoyant force acts through B
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C
OB=12 m
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D
Both (b) and (c)
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Solution

The correct options are
A The weight of the plank acts downwards at A
B The buoyant force acts through B
Weight of the body acts through its COM, ie mid point of the plank(A).

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

lcos45=hl=2h

OB=l2=h2=122

Physics

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