A cylindrical tank has a hole of diameter 2r in its bottom. The hole is covered wooden cylindrical block of diameter 4r, height h and density `rho//3`.

Situation I: Initially, the tank is filled with water of density `rho` to a height such that the height of water above the top of the block is `h_1` (measured from the top of the block).
Situation II: The water is removed from the tank to a height `h_2` (measured from the bottom of the block), as shown in the figure. The height `h_2` is smaller than h (height of the block) and thus the block is exposed to the atmosphere.
Find the height of the water level `h_2` (in situation 2), for which the block remains in its origin) position whithout the application of any external force

Options

A. (a) `h/3`
B. (b) `(4h)/(9)`
C. (c) `(2h)/(3)`
D. (d) `h`

Answer

B

Explanation

KEY CONCEPT:
Considering equilibrium of wooden block.
Total downward force =Total force upwards
Wt. of block+force due to atmospheric pressue=
Force due to pressure of liquid+Force due to atmospheric pressure
`pi(16r^2)rho/3xxg+P_0pixx16r^2=[h_2rhog+P_0]pi[(16-4)r^2]+P_0xx4r^2`
`implies4/9h=h_2`