Question

(9) If the force F(r) =r +3r?. Calculate the work done by this force in moving an object from r=0 to r = 3 m.
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Answer 1

Answer:

The gravitational force 'F' on satellite of mass 'm' revolving around the planet in the orbit of radius 'R' is

F=−

R

2

GMm

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=−∫

R

3R

Fdr

V=−

R

2

GMm

∫

R

3R

−(Fdr)

V=GMm∫

R

3R

R

2

1

dr

V=

R

GMm

−

3R

GMm

V=

3R

2GMm

Thus work done to increase the radius of orbit of satellite is

3R

2GMm