Question

A spherical ball of diameter $1\,cm$ and density $5\times10^3\, kg\, m^{-3}$ dropped gently in a large tank containing viscous liquid of density $3\times 10^3 kg\, m^{-3}$ and coefficient of viscosity $0.1\, Ns\, m^{-2}$.The distance, the ball moves in 1s after attaining terminal velocity is ($g \,=\, 10 \,ms^{-2}$)

• 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 $(d)=1\,cm =0.01\,m$
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 $(\sigma)=3 \times 10^{3} \,k\,gm ^{-3}$
Coefficient of viscosity $(\eta)=0.1\, Nsm ^{-2}$
We know that,
$v =\frac{2}{9} \frac{g r^{2}(\phi-\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} $
$v=\frac{10}{9} ms ^{-1}$
Now, $S=v t$
$S=\frac{10}{9} \times 1 $
$S=\frac{10}{9} m$