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Q.

If  the gravitational force between sun and earth is inversely proportional to  r3 , where r is distance between earth and sun. Then which of the following statements are correct.

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a

Its orbit around sun can’t be a stable elliptical orbit.

b

Its orbit around sun can’t be a stable circular orbit.

c

Motion of earth around sun will be in one plane.

d

Tidal forces acting on earth will be inversely proportional to  r4.

answer is A, B, C, D.

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Detailed Solution

1. Motion is in one plane by conservation of angular momentum
2.  mω2r=mv2r=(mvr)2mr3=L2mr3
 Question Image
Let equilibrium radius be   (L2mr03+Kr03)  or  K=L2m
In general force on earth
F=(L2mr3Kr3)dFdr=(3L2mr4+3Kr4) 
 dFdr=3(KL2m)[1r4)=0
This represents neutral equilibrium
3. Tidal forces are proportional to  dFdr

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