Question

State the factors on which the speed of a wave travelling along a stretched ideal string depends

Answer 1

Introduction:

The viscous force acting on a spherical body falling in a liquid with velocity v is F = 6πη r v. when a body falls in a liquid, it drags the layers of liquid with it downward while the fluid at large distance from the body remains unaffected. Thus a relative motion is produced among the layers of liquid.

Stoke’s Law

On the basis of experimental observations proof George stokes law concluded that the viscous force on a small sphere in a liquid depends upon:

Viscosity of liquid(η)Radius ( r )Speed of spherical bodyBy the method of dimensions

Or

Where K is a dimensionless constant.

Writing dimensions of F, η,r and v we get

Or

proof stokes law equating powers of both sides, we get

Substituting these values in equation (1), we get

F=K η r v

By experiments  K = 6 π

Viscous force, F=6 π η r v

This proof is well known stokes’ law. It holds for small spherical bodies in a homogenous viscous fluid.