JEE Main20262 April 2026Morning ShiftPhysicsGravitationActual
A planet (P₁) is moving around the star of mass 2M in the orbit of radius R . Another planet (P₂) is moving around another star of mass 4M in a orbit of radius 2R . Ratio of time periods of revolution of P₂ and P₁ is _______.
Options
- A1 2
- B2
- C4
- D1 4
Correct answer
B. 2
Step-by-step solution
Using Kepler's third law, the time period of revolution of a planet is given by T = 2 r^3 GM_s . For planet P₁ , the orbital radius is r = R and the mass of the star is M_s = 2M : T₁ = 2 R^3 G(2M) For planet P₂ , the orbital radius is r = 2R and the mass of the star is M_s = 4M : T₂ = 2 (2R)^3 G(4M) = 2 8R^3 4GM = 2 2R^3 GM Taking the ratio of T₂ and T₁ : T₂ T₁ = 2R^3 GM R^3 2GM = 2 2 = 2 Answer: 2