A binary star consists of two stars A (mass 2.2Mₛ) and B (mass 11Mₛ), where Mₛ is the mass of the sun. They are separated by distance r and are rotating about their centre of mass, which is stationary. What is the ratio of the total angular momentum of the binary star to the angular momentum of star B about the centre of mass?
Physics · Mixed Chapter
JEE Mains

Question

A binary star consists of two stars A (mass 2.2Mₛ) and B (mass 11Mₛ), where Mₛ is the mass of the sun. They are separated by distance r and are rotating about their centre of mass, which is stationary. What is the ratio of the total angular momentum of the binary star to the angular momentum of star B about the centre of mass?

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: About the common centre of mass, mₐ rₐ=mᵦ rᵦ, so rₐ/rᵦ=mᵦ/mₐ=11/2.2=5. Step 2: Both stars revolve with the same angular speed ω. Thus Lₐ=mₐ rₐ²ω and Lᵦ=mᵦ rᵦ²ω. Step 3: Lₐ/Lᵦ=(mₐ/mᵦ)(rₐ/rᵦ)²=(1/5)×25=5. Step 4: (Lₐ+Lᵦ)/Lᵦ=5+1=6.