A Spherical ball of radius $1 mm$ and density $10.5 g / cc$ is dropped in glycerine of coefficient of viscosity $9.8$ poise and density $1.5 g / cc$. Viscous force on the ball when it attains constant velocity is $3696 \times 10^{-x} N$. The value of $x$ is $\text { (Given, } g =9.8 m / s ^2 \text { and } \pi=\frac{22}{7} \text { ) }$

Give two uses of Stoke’s law.

A spherical ball is dropped in a long column of a highly viscous liquid. The curve in the graph shown, which represents the speed of the ball $(v)$ as a function of time $(t)$ is 

Consider two solid spheres $\mathrm{P}$ and $\mathrm{Q}$ each of density $8 \mathrm{gm} \mathrm{cm}^{-3}$ and diameters $1 \mathrm{~cm}$ and $0.5 \mathrm{~cm}$, respectively. Sphere $\mathrm{P}$ is dropped into a liquid of density $0.8 \mathrm{gm} \mathrm{cm}^{-3}$ and viscosity $\eta=3$ poiseulles. Sphere $Q$ is dropped into a liquid of density $1.6 \mathrm{gm} \mathrm{cm}^{-3}$ and viscosity $\eta=2$ poiseulles. The ratio of the terminal velocities of $\mathrm{P}$ and $\mathrm{Q}$ is 

A spherical solid ball of volume $V$ is made of a material of density $\rho_1$ . It is falling through a liquid of density $\rho_2 (\rho_2 < \rho_1 )$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$, i.e., $F_{viscous}= -kv^2 (k >0 )$,The terminal speed of the ball is 

In an experiment, a small steel ball falls through a Iiquid at a constant speed of $10\, cm/s$. If the steel ball is pulled upward with a force equal to twice its effective weight, how fast will it move upward ? ......... $cm/s$