Question

A small spherical ball of radius 0.1 mm and density 104 kg m-3 falls freely under gravity through a distance h before entering a tank of water. If, after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of h will be ______ m.
(Given g = 10 ms-2, viscosity of water = 1.0 × 10-5 N-sm-2).

Answer 1

The correct answer is 20
Speed after falling through height h, Should be equal to terminal velocity
$\sqrt{2gh}$ = terminal speed
$⇒ \sqrt{2gh} = \frac{2}{9} \frac{r²g(ρ-ρ′)}{η}$
$⇒ \frac{2}{9} × \frac{10^{-8} × 10 × 9000}{10^{-5}}$
$⇒ h = \frac{400}{2g}$
⇒ h = 20 m
Therefore , the value of h will be 20 m