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

Options

A. `(mv)/(2r)`
B. `(2mv)/r`
C. `(mv)/r`
D. `(mv)/(4r)`

Answer

C

Explanation

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