Question

A sphere of mass $m$ and radius $r$ is projected in a gravity free space with speed $v$. If coefficient of viscosity 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. none of these

Answer 1

Answer: (C)

$\frac{mV}{r}$

Using Stoke's law:
$F_{viscous}=6\pi \eta rv=ma$ since the body is in gravity free space.
$\therefore m\frac{dv}{dt}=6\pi \eta rv$
$\therefore m\frac{dv}{dx}\frac{dx}{dt}=6\pi \eta rv$
$\therefore m\frac{dv}{dx}v=6\pi \eta rv$
Putting $\eta =\frac{1}{6\pi }$
we get, $\therefore m\frac{dv}{dx}=r$
$\therefore m{\int }_0^{v}dv=r{\int }_0^{x}dx$
$x=\frac{mv}{r}$