First slide
Fluid statics
Question

A hemispherical portion of radius -R is removed from the bottom of a cylinder of radius R. The volume of remaining cylinder is V and its mass is M. It is suspended by a string in a liquid of density ρ, where it stays vertical. The upper surface of the cylinder is at a depth h below the liquid surface. The force on the bottom of the cylinder by the liquid is 

Difficult
Solution

 The net upward force on the bottom of the cylinder = weight of the liquid displaced by cylinder + thrust on the upper surface of cyliner due to i column of
liquid 
=Vρg+hρg×πR2=ρgV+πR2h

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