Question

A Spherical ball of radius $1 \,mm$ and density $10.5\, g / cc$ is dropped in glycerine of coefficient of viscosity $9.8$ poise and density $1.5 \,g / cc$. Viscous force on the ball when it attains constant velocity is $3696 \times 10^{-x} N$. The value of $x$ is_______ (Given, $g=9.8 \,m / s ^2$ and $\pi=\frac{22}{9}$ )

Answer 1

When the ball attain terminal velocity
$ F _{ v }=\left( mg - F _{ B }\right)(\because a =0) $
$ =\operatorname{V} \sigma_{ b } g - V \rho_{\ell} g $
$=\operatorname{Vg}\left(\sigma_{ b }-\rho_{\ell}\right) $
$=\frac{4}{3} \pi\left(10^{-3}\right)^3 \times 9.8(10.5-1.5) \times 10^3$
$ =3696 \times 10^{-7} N $
So , $x =7$