Two stars of masses m and 2 m at a distance d rotate about their common centre of mass in free space. The…

Two stars of masses m and 2m at a distance d rotate about their common centre of mass in free space. The period of revolution is
  1. 2πd33Gm
  2. 2π3Gmd3
  3. 12π3Gmd3
  4. 12πd33Gm

Solution

F=G2mmd2=2mω2d/3

Gmd2=ω2d3

ω2=3Gmd3

ω=3Gmd3

T=2πω=2πd33Gm

Asked in: JEE Main 2021 (24 Feb Shift 1)

Practice more Gravitation questions on Aicharya