A ball of radius $r $ and density $\rho$ falls freely under gravity through a distance $h$ before entering water. Velocity of ball does not change even on entering water. If viscosity of water is $\eta$, the value of $h$ is given by

A particle released from rest is falling through a thick fluid under gravity. The fluid exerts a resistive force on the particle proportional to the square of its speed. Which one of the following graphs best depicts the variation of its speed $v$ with time $t$ ?

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 $=10\,ms ^{-2}$ )

If the terminal speed of a sphere of gold ( density $= 19.5 kg/m^3$) is $0.2\ m/s$ in a viscous liquid (density $= 1.5\ kg/m^3$ ), find the terminal speed (in $m/s$) of a sphere of silver (density $= 10.5\ kg/m^3$) of the same size in the same liquid …… $m/s$

State stokes’ law. By using it deduce the expression for :

$(i)$ initial acceleration of smooth sphere and

$(ii)$ equation of terminal velocity of sphere falling freely through the viscous medium.

$(iii)$ Explain : Upward motion of bubbles produced in fluid.