Write $\mathrm{SI}$ and $\mathrm{CGS}$ unit of coefficient of viscosity.

An air bubble of diameter $6\,mm$ rises steadily through a solution of density $1750\,kg / m ^3$ at the rate of $0.35\,cm / s$. The co-efficient of viscosity of the solution (neglect density of air) is $……….\,Pas$ (given, $g =10\,ms ^{-2}$)

The terminal velocity of a small sphere of radius $a$ in a viscous liquid is proportional to

A spherical body of radius $R$ consists of a fluid of constant density and is in equilibrium under its own gravity. If $P ( r )$ is the pressure at $r ( r < R )$, then the correct option$(s)$ is(are)

$(A)$ $P ( I =0)=0$ $(B)$ $\frac{ P ( r =3 R / 4)}{ P ( r =2 R / 3)}=\frac{63}{80}$

$(C)$ $\frac{ P ( r =3 R / 5)}{ P ( r =2 R / 5)}=\frac{16}{21}$ $(D)$ $\frac{ P ( r = R / 2)}{ P ( r = R / 3)}=\frac{20}{27}$

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.