A binary star consists of stars A and B of masses 2.2Mₛ and 11Mₛ, respectively, where Mₛ is the Sun's mass. They are separated by distance d and rotate about their stationary centre of mass. Find the ratio of the total angular momentum of the binary system to the angular momentum of star B.
Physics · Gravitation · Satellites, Orbital Motion & Kepler’s Laws
JEE Mains Advanced

Question

A binary star consists of stars A and B of masses 2.2Mₛ and 11Mₛ, respectively, where Mₛ is the Sun's mass. They are separated by distance d and rotate about their stationary centre of mass. Find the ratio of the total angular momentum of the binary system to the angular momentum of star B.

Physics · Gravitation · Satellites, Orbital Motion & Kepler’s Laws

G1 Physics · Accepted Answer

Step 1: Treat the two-star system as circular motion about the common centre of mass. The separation d obeys ω² = G(M₁+M₂)/d³. Step 2: Use r₁:r₂ = M₂:M₁ for the individual orbital radii; energy and angular momentum follow from v=ωr. Step 3: Apply the stated mass/radius change and simplify. Final: 6.