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

Answer

B

Explanation

Force from right and side of the liquid on left hand side liquid.
i. Due to surface tension force `=2RT` (towards right)
ii. Due to liquid pressure force
`=int_(x=0)^(x=h)(p_(0)+rhogh)(2Rx)dx`
`=(2p_(0)Rh+Rrhogh^(2))` (towards left)
`:.` Net force is `| 2p_(0)Rh+r rhogh^(2)-2RT|`