A sphere of radius and density is released from the surface of a liquid of density…

PHYSICS · Single correct · CBSE · Physics · Mechanical Properties of Fluids · Mechanical Properties of Fluids

Problem

A sphere of radius

r

and density

\rho

is released from the surface of a liquid of density

\frac{\rho}{2}

and coefficient of viscosity

\eta

. It achieves terminal velocity just before reaching the ground. Then choose the correct option(s). (a) Terminal velocity is

\frac{2r^2 \rho g}{9\eta}

(b) Terminal velocity is

\frac{r^2 \rho g}{9\eta}

\frac{2\pi r^3 \rho g}{3} \left( H - \frac{\rho^2 r^4 g}{81\eta^2} \right)

(d) Magnitude of work done by viscous force on the sphere is

\frac{4}{3} \pi r^3 \rho g \left( H - \frac{\rho^2 r^4 g}{9\eta^2} \right)