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 the section by water( the other side of this section has magnitude

Options

A. ` |2 P_0 Rh + pi R^ 2 rho gh - 2 RT | `
B. `|2 P_0 Rh + Rrho gh ^ 2 - 2 RT| `
C. ` | P_0 pi R^2 + R rho gh ^ 2 - 2 RT | `
D. `|P_0 pi R^ 2 + R rho gh ^ 2 + 2 RT | `

Answer

B

Explanation

Force from right hand side of the liquid on left hand side liquid.
(i) Due to surface tension force (towards right)
(ii) Due to liquid pressure force `=overset(x=h)underset(x=0)(int)(P_(0)+rhogx)(2R)dx=(2P_(0)Rh+Rrhogh^(2))` (towards left)
`therefore" ""Net force is "|2P_(0)Rh+Rrhogh^(2)-2RT|`