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)

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

$r^{4}$

$r^{2}$

$r^{3}$

$r$

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Velocity of the ball after free fall : $V = \sqrt{2 g h}$
given it is equivalent to terminal velocity in a liquid
$\begin{array}{l} m g - B = F_{d r a g} \\ \Rightarrow ρ \frac{4}{3} π r^{3} g - J \frac{4}{3} π r^{3} g = 6 π η r V_{T} \\ \Rightarrow (ρ - J) \frac{4}{3} π r^{2} g = 6 π η \sqrt{2 g h} \\ \Rightarrow h \propto r^{4} \end{array}$

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE