Water is filled up to a height `h` in a beaker of radiys `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 on this section by water on the other side of this section has magnitude

Options

A. `[2P_(0)Rh+piR^(2)pgh-2RT]`
B. `[2P_(0)Rh+Rpgh^(2)-2RT]`
C. `[P_(0)piR^2+Rpgh^(2)-2RT]`
D. `[P_(0)piR^2+Rpgh^(2)+2RT]`

Answer

B

Explanation

We can select a strip of width dx at a depth x to write force on it due to pressure and then can integrate to get the total force. Force due to surface tension is T(2R) and is opposite to force due to pressure. Hence net force can be written as follows :
`F=[ underset(0)overset(h)int (P_(0)+pgx) (2Rdx)]-2RT`
`rArr F=2P_(0)Rh+Rpgh^(2)-2RT`