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 minimum value of height `h_1` (in situation 1), for which the block just starts to move up?

Options

A. `2h//3 `
B. `5h//4 `
C. `5h//3 `
D. `5h//2`

Answer

C

Explanation

` P_(atm ) pi r ^ 2 + [P_(atm ) + (h+ h_1 ) rho g ] 3pi r ^ 2 `
` m g + (P_(atm) + h _ 1 rho g ) 4pi r ^2 `
Where ` mg = 4pi r ^2 h (rho )/(3) g `
Where N = 0
` rArr P_(atm ) pi r ^ 2 + [ P_(atm ) + (h + h _ 1 ) rho g ] 3 pi r ^2 = m g + (P_(atm ) + h _ 1 rho g ) 4pi r ^2 rArr h _ 1 = (5)/(3) h ` i.e, Option (C )