In an experiment to verify Stokes law, a small spherical ball of radius $r$ and density $\rho$ falls under gravity through a distance $h$ in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of $h$ is proportional to :

(ignore viscosity of air)

A sphere is dropped under gravity through a fluid of viscosity $\eta$ . If the average acceleration is half of the initial acceleration, the time to attain the terminal velocity is ($\rho$ = density of sphere ; $r$ = radius)

From amongst the following curves, which one shows the variation of the velocity v with time t for a small sized spherical body falling vertically in a long column of a viscous liquid

A water drop of radius $1\,\mu m$ falls in a situation where the effect of buoyant force is negligible. Coefficient of viscosity of air is $1.8 \times 10^{-5}\,Nsm ^{-2}$ and its density is negligible as compared to that of water $10^{6}\,gm ^{-3}$. Terminal velocity of the water drop is________ $\times 10^{-6}\,ms ^{-1}$

(Take acceleration due to gravity $=10\,ms ^{-2}$ )

A copper ball of radius $'r'$ travels with a uniform speed $'v'$ in a viscous fluid. If the ball is changed with another ball of radius $'2r'$ , then new uniform speed will be

Velocity of water in a river is