Question

In an experiment, a small steel ball falls through a liquid at a constant speed of $10cm/s$. If the steel ball is pulled upward with a force equal to twice its effective weight, how fast will it move upward ?

• A. 5 cm/s
• B. Zero
• C. 10 cm/s
• D. 20 cm/s

Answer 1

Answer: (C)

Weight of the body
$W=mg=\frac{4}{3}\pi r^3\rho g$
$T=\frac{4}{3}\pi r^3\sigma g$
andF =$6\pi \eta vr$
When the body attains terminal velocity net force acting on the body is zero, i.e.,
$W-T-F=0$
And terminal velocity $v=\frac{2}{9}\frac{r^2\left(\rho -\sigma \right)g}{\eta }$
As in case of upward motion upward force is twice its effective weight, therefore, it will move with same speed $10cm/s$