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 + tank is `W_(1)` and that of hemisphere is`'W_(2)`. W Then choose the incorrect options

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, taken by a weighing machine is equal to `W_(1)+W_(2)`

Explanation

(a) Force on flat surface depends on H
(b) Pressure at the location of curved surface depends on H
(c) Net force on hemisphere by liquid `=(2/3 piR^(3))(rho)g`