A solid rubber ball of density d and radius E falls vertically through air. Assume that the air resistance acting on the ball is F = kRV, where k is constant and V its velocity. Because of this air resistance, the ball attains a constant velocity called terminal velocity V_t after some time. Then V_t is

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

$\frac{4 {πR}^{2} dg}{3 k}$

$\frac{4 {πRd}^{2} g}{3 k}$

$\frac{4 {πRdg}^{2}}{3 k}$

$\frac{4 πRdg}{3 k}$

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

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

Take Free Test

Detailed Solution

The ball attains the terminal velocity when the resultant force acting on the ball is zero. This happens when air resistance F acting upwards is exactly equal to the weight m g of the ball acting vertically downwards.

$∴ {kRV}_{t} = mg = (\frac{4}{3} {πR}^{3} d) g$

or $V_{t} = \frac{4 {πR}^{2} d^{'} g}{3 k}$

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

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 Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th