Question

A spherical ballof radius $3.0\times {10}^{-4}m$ and density ${10}^4$ $kg/m^3$ falls freely under gravity through a distance h it before entering a tank of water (coefficient of viscosity = $\eta$ = $9.8\times {10}^{-6}Ns{m}^{-2}$ and density = ${10}^{3}kg/m^3$. If after entering the water, the velocity of the ball does not change, find~h.(Take g =9.8 $m{s}^{-2}$)

• A. 10.24 m
• B. 1.65 km
• C. 32.36 m
• D. 50.12 m

Answer 1

The correct option is B 1.65 km

Terminal velocity,

$u=\sqrt{2gh}=\frac{2r^2(\rho -\sigma )g}{9\eta }\Rightarrow h=\frac{2g{r}^4(\rho -r{)}^2}{81{\eta }^2}=1.65km$