The height of water in a vessel is h. The vessel wall of width b is at an angle `theta` to the vertical. The net force exerted by the water on the wall is

Options

A. `(1)/(3) rho bh^(2)g costheta`
B. `(1)/(2b)h^(2)rhog`
C. `(1)/(2)rhobh^(2)g sectheta`
D. Zero

Answer

C

Explanation

`z=y sec theta`
`dz=dy sec theta`
`p=(rho g y)`
`dA=(b)dz=(b)dy sec theta`
`dF=pdA=(rho gb sec theta)y dy`
`:. F=int_(0)^(h)dF=1/2rhobh^(2)g sec theta`.