Question

A sphere of mass $m$ and radius $r$ is projected along a straight line in a gravity free space with speed $v$. If the coefficient of viscosity of the medium in which it moves is $\frac{1}{6\pi }$, then the distance travelled by the body before it stops is

• A. $\frac{mv}{2r}$
• B. $\frac{2mv}{r}$
• C. $\frac{mv}{r}$
• D. $\frac{mv}{4r}$

Answer 1

The correct option is C $\frac{mv}{r}$

As the sphere is projected in the medium in gravity free space, thus, only drag force or viscous force will act on it.
$\Rightarrow F=-6\pi r\eta v$
$\Rightarrow F=-rv$ $[$ given, $\eta =\frac{1}{6\pi }]$
$\Rightarrow ma=-rv$
$\Rightarrow mv\frac{dv}{dx}=-rv$
$\Rightarrow mdv=-rdx$
On integrating both side,
$\Rightarrow m{\int }_v^{0}dv=-r{\int }_0^{x}dx$
$\Rightarrow m(0-v)=-r(x-0)$
$\Rightarrow -mv=-rx$
$\Rightarrow x=\frac{mv}{r}$