Question

A spherical ball of diameter $1cm$ and density $5\times 10^{3}kg{m}^{-3}$ dropped gently in a large tank containing viscous liquid of density $3\times 10^{3}kg{m}^{-3}$ and coefficient of viscosity $0.1Ns{m}^{-2}$.The distance, the ball moves in 1s after attaining terminal velocity is ($g=10m{s}^{-2}$)

• A. $\frac{10}{9}m$
• B. $\frac{2}{3}m$
• C. $\frac{4}{9}m$
• D. $\frac{4}{5}m$
• E. $\frac{9}{10}m$

Answer 1

Answer: (A)

Given, diameter of spherical ball $(d)=1cm=0.01m$
Radius of spherical ball $(r)=\frac{0.01}{2}m$
Density of spherical ball $(\rho )=5\times 10^{3}kg{m}^{-3}$
Density of liquid $(\sigma )=3\times 10^{3}kg{m}^{-3}$
Coefficient of viscosity $(\eta )=0.1Ns{m}^{-2}$
We know that,
$v=\frac{2}{9}\frac{g{r}^2(\varphi -\sigma )}{\eta }$
$v=\frac{2\times 10\times (0.01{)}^2\times \left(5\times 10^3-3\times 10^3\right)}{9\times (2{)}^2\times 0.1}$
$v=\frac{10}{9}m{s}^{-1}$
Now, $S=vt$
$S=\frac{10}{9}\times 1$
$S=\frac{10}{9}m$