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

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

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)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

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
$\Rightarrow \frac{3}{4 m g R} + W_{r} = \frac{3}{8} m g R \Rightarrow W_{r} = \frac{- 3}{8} m g R$