Question

A spherical ball of density $\rho$ and radius 3 mm is dropped into a tube containing a viscous liquid filled a upto 0 mark as shown in the figure. Viscosity of the liquid is 1.260 $N-s/m^2$ and its density is ${\rho }_L=\rho /2=1260kg/m^3$. Assume the ball reaches a terminal speed by the 10 cm mark. The time taken by the ball to travel the distance between the 10 cm and 20 cm mark is
(take g= 10 $m/s^2$)

• A. 500 $\mu s$
• B. 50 ms
• C. 0.5 sec
• D. 5 sec

Answer 1

The correct option is D 5 sec

We know that terminal velocity $v=\frac{2({\rho }_{metal}-{\rho }_{fluid}g{R}^2}{9\mu }$

Here $R=3\times {10}^{-3}m$

Putting the value we get ${\rho }_{metal}-{\rho }_{fluid}={\rho }_{metal}/2$

We know that terminal velocity $v=\frac{21260\times g\times 9\times {10}^{-6}}{18\times 1.2160}$

$v=2\times {10}^{-2}m/s$

Distance traveled $=10cm=0.1m$

$t=\frac{0.1}{v}=5sec$