Question

A hemispherical portion of radius R is removed from the bottom of a cylinder of radius R. The volume of the 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

• A. Mg
• B. Mg – V ρg
• C. Mg + πR²hρg
• D. ρg(V +πR²h)

Answer 1

Answer: (D)

ρg(V +πR²h)

Answer 2

Using Archimede’s principle,

F_bottom - hρg(πR²) = Vρg

(ignoring atmospheric pressure)

Therefore (4).