Question

Two point masses of mass m₁ = fM and m₂ = (1 - f) M (f < 1) are in outer space (far from gravitational influence of other objects) at a distance R from each other. They move in circular orbits about their centre of mass with angular velocities ω₁ for m₁ and ω₂ for m₂. In that case ______.

Options

• (1 - f)ω₁ = fω

• ω₁ = ω₂ and independent of f.

• fω₁ = (1 - f)ω₂

• ω₁ = ω₂ and depend on f.

Answer 1

Two point masses of mass m₁ = fM and m₂ = (1 - f) M (f < 1) are in outer space (far from gravitational influence of other objects) at a distance R from each other. They move in circular orbits about their centre of mass with angular velocities ω₁ for m₁ and ω₂ for m₂. In that case ω₁ = ω₂ and independent of f.

Explanation:

Angular velocity is the angular displacement per unit time i.e., ω = `(Deltatheta)/(Deltat)`

Here ω₁ = ω₂ and independent of f.