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Two Point masses of mass $m_{1} = fM$ and $m_{2} = (1 - f) M (f < 1)$ 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 $ω_{1}$ for m₁ and $ω_{2}$ for m₂. If that case

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$(1 - f) ω_{1} = {fω}_{2}$

$ω_{1} = ω_{2}$ and independent of f

${fω}_{1} = (l - f) ω_{2}$

$ω_{1} = ω_{2}$ and depend on f

answer is B.

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Detailed Solution

$ω = \frac{dθ}{dt}$

net force on the system is zero, so the centre of mass will not change.

these two masses will always be in opposite direction with respect to centre of mass and sweep equal angles around the centre.

hence, $ω_{1} = ω_{2} = \frac{d θ}{d t}$ and it will be independent of mass fraction 'f'.

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