If the terminal velocity of a metal sphere of mass $8 \ g$ falling through a liquid is $3 \ cm s^{-1}$, then the terminal velocity of another sphere of mass $64 \ g$ made of the same metal falling through the same liquid is (in $cm s^{-1}$)

State Stokes' law. By using it,deduce the expression for:
$(i)$ Initial acceleration of a smooth sphere.
$(ii)$ Equation of terminal velocity of a sphere falling freely through a viscous medium.
$(iii)$ Explain: Upward motion of bubbles produced in a fluid.

In the measurement of viscosity of liquids using terminal velocity experiment, spherical balls of same radius but having different densities are used. The variation of the terminal velocity $(v)$ with the ratio of density of spherical ball $(\sigma)$ to density of the liquid $(\rho)$, is best represented by :

Eight equal drops of water are falling through air with a steady speed of $10\,cm/s$. If the drops coalesce,the new velocity is $.........\,cm/s$.

We have three beakers $A, B$,and $C$ containing glycerine,water,and kerosene respectively. They are stirred vigorously and placed on a table. The liquid which comes to rest at the earliest is

Give two uses of Stoke's law.