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Water is filled up to a height h in a be...

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

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)+Rrhogh^(2)-2RT|`

Text Solution

Verified by Experts

The correct Answer is:
B
Pushing force `= ltpgt` (Area)
`= (((p_(0))+(p_(0)+rhogh))/(2))(2Rh)`
`= 2p_(0)Rh + rhogh^(2)R`
Pulling force `= (T)(2R)`
Net force `= |2p_(0)Rh + rhogh^(2)R - 2TR|`
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