In an experiment to verify Stokes law, a small spherical ball of radius r and density ρ falls under gravity through a distance h in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of h is proportional to (ignore viscosity of air)

Question

In an experiment to verify Stokes law, a small spherical ball of radius r and density ρ falls under gravity through a distance h in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of h is proportional to (ignore viscosity of air) (A) r (B) r 4 (C) r3 (D) r2

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/48925657fb0632cc63dc3d1250a25c51-.png" /> After falling through h , the velocity be equal to terminal velocity √2 gh =(2/9) ( r 2 g /η)(ρℓ-ρ) ⇒ h =(2/81) ( r 4 g (ρℓ-ρ)2/η2) ⇒ h propto r 4

$r$

$r^{4}$

$r^{3}$

$r^{2}$

After falling through $h,$ the velocity be equal to terminal velocity
$2 g h = \frac{2}{9} \frac{r ^{2} g}{η} (ρ_{ℓ} - ρ)$
$\Rightarrow h = \frac{2}{81} \frac{r ^{4} g ( ρ _{ℓ} - ρ ) ^{2}}{η ^{2}}$
$\Rightarrow h \propto r^{4}$

r

r4

r3

r2

After falling through h, the velocity be equal to terminal velocity 2gh​=92​ηr2g​(ρℓ​−ρ) ⇒h=812​η2r4g(ρℓ​−ρ)2​ ⇒h∝r4

$r$

$r^{4}$

$r^{3}$

$r^{2}$

After falling through $h,$ the velocity be equal to terminal velocity
$2 g h = \frac{2}{9} \frac{r ^{2} g}{η} (ρ_{ℓ} - ρ)$
$\Rightarrow h = \frac{2}{81} \frac{r ^{4} g ( ρ _{ℓ} - ρ ) ^{2}}{η ^{2}}$
$\Rightarrow h \propto r^{4}$