Question

A solid hemisphere of radius `R` is made to just sink in a liquid of density `rho`. Find a. the vertical thrust on the curved surface b. the vertical thrust on the flat surface c. the side thrust on the hemisphere. d. the total hydrostatic force acting on the hemisphere.

A. `(piR^(3)rhog)/(3)`
B. `(piR^(3)rhog)/(2)`
C. 0
D. `piR^(3)rhog`

Answer 1

Correct Answer - A

Vertical thrust of the liquid is equal to weight of the liquid column above the curve (sphericalj) surface.
`F_(V)=vrhog`. Volume of the shaded portion
`=(piR^(3))-(2)/(3)piR^(3)=(piR^(3))/(3)`
Substituting V in te equation `F_(V)=Vrhog`, we have `F_(V)=(piR^(3))/(3)rhog` (down)