Water is filled up to a height h in a beaker of radius R as shown in the figure. The density of water is `rho,` the surface tension of water is T and the atmospheric pressure is `P_0.` Consider a vertical section ABCD of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude

Options

A. `[2P_(0)Rh+ppi R^(2)rho gh-2 RT]`
B. `[2 P_(0)Rh+R rho gh^(2)-2 RT]`
C. `[P_(0)piR^(2)+R rho gh^(2)-2 RT]`
D. `[P_(0)pi R^(2)+R rho gh^(2)+2 RT]`

Answer

B

Explanation

Force due to pressure of water, i.e. ,

`F_(P)=int_(0)^(h)(P_(0)+rho gy)(2 Rdy)`
(as force = Pressure x Area)
`=int_(0)^(h) P_(0)2R dy +int_(0)^(h)rho g Rh^(2)`
Force due to surface tension, i.e., `F_(T)=T(2R)= RT`
Net force from one side, `F_("net")=F_(p)-F_(T)=2P_(0)Rh+rho g Rh(2)- 2 RT`