According to Stoke, the viscous force experienced by a sphere of radius r depends on the terminal velocity and viscosity of the liquid besides radius. Derive the formula

Viscous force on small sphere of radius R moving in fluid varies as

The ternimal velocity of small sized spherical ball of radius r falling vertically in a viscous liquid is

Using Stokes' Law show that the constant terminal velocity v of a sphere of radius r, density rho falling vertically under gravity through a viscous fluid of density sigma and co-efficient of viscosity eta is given by- v = (2/9).[{r^2g(rho - sigma)}/eta]

A ball of mass m and radius r is released in a viscous fluid. The value of its terminal velocity is proportional to

When a sphere of radius r rolls with its COM having a linear velocity v, what is the velocity of (i) the lower-most point in contact with the surface and (//) the top-most point?

In Millikan’s oil drop experiment, what is the terminal speed of an uncharged drop of radius 2.0 xx 10^-5m and density 1.2 xx 10^3 kg m^-3 ? Take the viscosity of air at the temperature of the experiment to be 1.8 xx 10^-5 Pa s. How much is the viscous force on the drop at that speed? Neglect buoyancy of the drop due to air.

A rain drop of radius 2 mm falls from a height of 500 m above the ground. It falls with decreasing acceleration (due to viscous resistance of the air) until at half its original height, it attains its maximum (terminal) speed, and moves with uniform speed thereafter. What is the work done by the gravitational force on the drop in the first and second half of its journey? What is the work done by the resistive force in the entire journey if its speed on reaching the ground is 10 m s-^1 ?

Prove the result that the velocity v of translation of a rolling body (like a ring, disc, cylinder or sphere) at the bottom of an inclined plane of a height h is given by v^2=(2gh)/ (i+k^2^l R^3 Using dynamical consideration (i.e. by consideration of forces and torques). Note k is the radius of gyration of the body about its symmetry axis, and R is the radius of the body. The body starts from rest at the top of the plane.

The terminal velocity of a copper ball of radius 2.0 mm falling through a tank of oil at 20^@C is 6.5 cm/s. Compute the viscosity of the oil at 20^@C . Given, rho_(oil) = 1.5 xx 10^3 kg//m^3, rho_(copper) = 8.9 xx 10^3 kg//m^3 .

A sphere of radius 0.25mm and of density 9000kg/m^3 falls through an oil of co-efficient of viscosity 0.2 Ns/m^2 and of density 800kg/m^3 . Find the terminal velocity of the sphere.