A test particle is moving in a circular orbit in the gravitational field produced by a mass density ρ r…

A test particle is moving in a circular orbit in the gravitational field produced by a mass density ρr=Kr2. Identify the current relation between the radius R of the particle’s orbit and its period T:
  1. TR is a constant
  2. T2R3 is a constant
  3. TR is a constant
  4. TR2 is a constant

Solution

M=∫ρ4πr2dr
=∫0RKr24πr2dr
=4πKR
Satellite velocity =GMR=4πK
Time period, T=2πRv=2πR4πK
Now,
TR=2π4πK= constant

Asked in: JEE Main 2019 (09 Apr Shift 2)

Practice more Gravitation questions on Aicharya