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Question

Imagine a light planet revolving around a very massive star in a circular orbit of radius r with a period of revolution T. If the gravitational force of attraction between the planet and the star is proportional to r5/2, then the square of the time period will be proportional to.
  1. r3
  2. r2.5
  3. r2
  4. r3.5

A
r3
B
r2
C
r2.5
D
r3.5
Solution
Verified by Toppr

Gravitational force,FG1r5/2
revolvong in circular orbit, so, FG=centripetal force
Centripetal forcer5/2
mrω2r5/2
Mass is constant, so,
ω2r5/2r
ω2r7/2ω=2πT
(2πT)2r7/2
T2r7/2

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