Figure shows a large closed cylindrical tank containing water. Initially, the air trapped above the water surface has a height `h_(0)` and pressure `2p_(0)` where `rh_(0)` is the atmospheric pressure. There is a hole in the wall of the tank at a depth `h_(1)` below the top from which water comes out. A long vertical tube is connected as shown.

Find the height `h_(2)` of the water in the long tube above top initially.

Options

A. ` (3 p_0 ) / (rho g ) - (h_0)/(3 ) `
B. ` (2 p _ 0)/(rho g ) - (h_0)/(2 ) `
C. ` (p_0)/( rho g ) - h_0 `
D. ` (p_0)/(2 rho g ) - 2 h_0 `

Answer

C

Explanation

`2P_(0)=(h_(2)+h_(0))rhog+P_(0)` (Since liquids at the same level have the same pressure)
`RightarrowP_(0)=h_(2)rhog+h_(0)rhog" "Rightarrow" "h_(2)=(P_0)/(pg)-h_(0)`