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. `|2P_(0)Rh+piR^(2)rhogh-2RT|`
B. `|2P_(0)Rh+Rrhogh^(2)-2RT|`
C. `|P_(0)piR^(2)+Rrhogh^(2)-2RT|`
D. `|P_(0)piR^(2)+Rrhogh^(2)-2RT|`

Answer

B

Explanation

Let us find the force exerted on water in the right side of section ABCD.
This force F = force `F_(1)` due to pressure on the left side of section ABCD `+` force `F_(2)` due to surface tension. Now
`F_(1)` = pressure at the centre `xx` area of ABCD
`F_(1)=(P_(0)+(h)/(2)rhog)xx2Rh` directed towards right
`F_(2)` = surface tension `xx` length AB `impliesF_(2)=Txx2R=2RT` directed toward left
`therefore F = (P_(0)+(h)/(2)rhog)xx2Rh-2RT" "impliesF=[2P_(0)Rh+Rrhogh^(2)-2RT]`