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 1: 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 2: 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 original position without the application of any external force.

Options

A. ` h//3 `
B. `4h//9 `
C. `2h//3 `
D. `h`

Answer

B

Explanation

For equilibrium ` (N = 0 ) `,
` P_(atm) pi r ^ 2 + (P_(atm) + h _ 2 rho g ) 3pi r ^ 2 = P_(atm ) (4pi r ^ 2 ) + 4pi r ^2 (h rho g ) /(3 ) rArr h _ 2 = ( 4h )/(9) ` i.e. Option (B) is correct.