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Question

The work done to increase the radius of orbit of a satellite of mass m revolving around a planet of mass M from orbit of radius R into another orbit of radius 3R is :
  1. 2GMm3R
  2. GMmR
  3. GMm6R
  4. GMm24R

A
2GMm3R
B
GMm6R
C
GMmR
D
GMm24R
Solution
Verified by Toppr

The gravitational force 'F' on satellite of mass 'm' revolving around the planet in the orbit of radius 'R' is
F=GMmR2
Where
G is gravitational constant
M is Mass of the planet.
The work done in increasing the radius of orbit of the satellite through 'dr' is
W=Fdr
but work done is equal to change in gravitational potential 'dV'
therefore
dV=Fdr
V=3RRFdr
V=GMmR23RR(Fdr)
V=GMm3RR1R2dr
V=GMmRGMm3R
V=2GMm3R
Thus work done to increase the radius of orbit of satellite is 2GMm3R

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