GATE Civil Engineering (CE) 2019 Shift 2 Solved Paper

A solid sphere of radius, $\mathit{r}$, and made of material with density ${\mathit{\rho }}_{\mathit{s}}$, is moving through the atmosphere (constant pressure, p) with a velocity, $\mathit{v}$. The net force ONLY due to atmospheric pressure $\left({\mathit{F}}_{\mathit{p}}\right)$ acting on the sphere at any time, $\mathit{t}$, is