A sphere of mass m and radius r is projected in a gravity free space with speed v. If coefficient of viscosity of the medium in which it moves is `1/(6pi)` , the distance travelled by the body before it stops is

Options

A. `(mv)/(2r)`
B. `(mv)/(2r)`
C. `(mv)/(r)`
D. none of these

Answer

C

Explanation

The only force acting on the body is the viscous force
Here, `m(vdv)/(dx) = -6 pi eta rv = -rv`
`rArr underset(v) overset(0)int mdv = underset(0)overset(x)int - rdx rArr x = (mv)/(r)`