An artificial satellite of mass m revolves in a circular orbit of radius 4R around the centre of the moon (where R is the radius of the moon). Suddenly it starts experiencing a slight resistance due to cosmic dust. The resistance force depends on the speed of satellite as F = kv where k is a constant. If the radius of the moon is R and acceleration due to gravity on the moon’s surface is g, then (assume that at every moment the satellite follows a circular path)

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

The satellite will hit the moon’s surface after time $t = \frac{m}{k} \ln 2$

Work done by gravitational force till the satellite hits the moon’s surface $= \frac{3}{4} m g R .$

The satellite will hit the moon’s surface after time $t = \frac{2 m}{k} \ln 2$

The work done by the resistance force on the satellite till it hits the moon surface $= - \frac{3}{8} m g R .$

answer is A, C, D.

(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

for circular orbit of satellite
$E = \frac{U}{2} = - K \Rightarrow - d E = d K \Rightarrow (k v) v d t = m v d v$
$\frac{d v}{d t} = \frac{k v}{m} \Rightarrow \int d t = - \frac{m}{k} \int_{v_{1}}^{v_{1}} \frac{d v}{v} \Rightarrow t = \frac{m}{k} I n (\frac{v_{r}}{v_{i}}) = \frac{m}{k} I n \sqrt{\frac{G M / R}{G M 4 R}} = \frac{m}{k} I n 2$
Question Image
$\Rightarrow \frac{3}{4 m g R} + W_{r} = \frac{3}{8} m g R \Rightarrow W_{r} = \frac{- 3}{8} m g R$