How will the weight of a body be affected, when it falls with its terminal velocity through a viscous medium?

The terminal velocity of a sphere moving through a viscous medium is :

The terminal velocity of a sphere moving through a viscous medium is :

How is the terminal velocity of a body related with the coefficient of viscosity of a viscous medium?

A small spherical ball falling through a viscous medium of negligible density has terminal velocity v. Another ball of the same mass but of radius twice that of the earlier falling through the same viscous medium will have terminal velocity

A small spherical ball falling through a viscous medium of negligible density has terminal velocity v. Another ball of the same mass but of radius twice that of the earlier falling through the same viscous medium will have terminal velocity

Derive an expression for terminal velocity of the sphere falling under gravity through a viscous medium.