There are two identical small holes of area of cross-section a on the opposite sides of a tank containing a liquid of density `rho`. The difference in height between the holes is h. Tank is resting on a smooth horizontal surface. Horizontal force on which will have to be applied on the to keep it in equilibrium is

Options

A. `sqrt(h)`
B. h
C. `h^(3//2)`
D. `h^(2)`

Answer

B

Explanation

Net horizontal force (reaction) `=F=F_(B)-F_(A)=(dp_B)/(dt)=(dp_(A))/(dt)`
`=av_(B)pxxv_(B)-av_(A)pxxv_(A)`
`therefore F=ap(v_(B)^(2)-v_(B)^(2))...(i)`
According to Bernoulli's theoram
`P_(A)+(1)/(2)pv_(A)^(2)+pgh=p_(B)+(1)/(2)pv_(B)^(2)+(p_(A-p)-p_(B))`
`Rightarrow (1)/(2)(v_(B)^(2)-v_(B)^(2))=pgh Rightarrow v_(B)^(2)-v_(A)^(2)=2gh`
`"From equaiton" (i), F=2apgh Rightarrow Falpha h `