A sphere is just immersed in a liquid. Find the ratio of hydrostatic force acting on top and bottom half of the sphere.

Answer

`1/5`

Explanation

Volume `V_(1)` of the super incument liquid of the upper hemisphere.

`V_(1)=piR^(2).R=2/3piR^(3)=(piR^(3))/3`
Then the hydrostatic force acting on the upper hemisphere
`h_(1)rhoV_(1)g=(piR^(2)rhog)/3`
Then `F_(2)-F_(1)=F_(b)` or `F_(2)=F_(b)+F_(1)=5/3piR^(3)rhog`
Then `(F_(1))/(F_(2))=1/5`