# Sphere in Swimming Pool

**Classical Mechanics**Level 5

Find The net upward Force exerted by the liquid of an Swimming Pool on the uniform sphere on **bottom half sphere**.
Neglect atmospheric pressure . If Radius of sphere is 'R' and it is at the depth 'h'
from the upper upper surface of swimming pool. And density of liquid is \(\rho \)
It can be Express as :
\({ F }_{ upward }\quad =\quad \cfrac { a }{ b } \pi \rho g{ R }^{ c }\)

Find a + b + c