Question

A solid glass hemisphere of density $d$ and radius $R$ lies (with curved surface of hemisphere below the flat surface) at the bottom of a tank filled with water of density $\rho$ such that the flat surface of hemisphere is $H$ depth below the liquid surface. Weight of water and tank is $W_1$ and that of hemisphere is $W_2$. Then choose the incorrect options

• A. Force exerted by the liquid on the flat surface of hemisphere is independent of H and $d$ but depends on $R$ and $\rho$
• B. Force exerted by the liquid on the curved surface of hemisphere is independent of $H$ and $d$ but depends on R and $\rho$
• C. Force exerted by the liquid on the hemisphere is independent of $H$ and d but depends on $R$ and $\rho$
• D. Combined weight of water $+$ tank $+$ hemisphere (with hemisphere inside water) placed on a weighing machine is equal to $W_1+W_2$

Answer 1

Answer: (A), (B)

The correct options are
A Force exerted by the liquid on the flat surface of hemisphere is independent of H and $d$ but depends on $R$ and $\rho$
B Force exerted by the liquid on the curved surface of hemisphere is independent of $H$ and $d$ but depends on R and $\rho$



(a) force on flat surface depends on H as $F=(P_0+\rho gH)A$

(b) Pressure at the location of curved surface depends on H as $P=P_0+\rho gH$

(c) Net force on hemisphere by liquid $=\left(\frac{2}{3}\pi R^3\right)\left(\rho \right)g$ = force of buoyancy