A binary star is a system of two stars rotating about their centre of mass only under their mutual gravitational attraction. Let the stars have masses $m$ and $2 m$ and let their separation be $l$ . Their time period of rotation about their centre of mass will be proportional to

l^{3 / 2}

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l

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m^{1 / 2}

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m^{- 1 / 2}

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Solution

The correct options are
B $l^{3 / 2}$
D $m^{- 1 / 2}$
$F = G \frac{m (2 m)}{l^{2}} = m ω^{2} (2 l / 3)$
or $\frac{3 m G}{l^{3}} = ω^{2} . T = \frac{2 π}{ω} = 2 π \sqrt{\frac{l^{3}}{3 m g}}$

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A binary star is a system of two stars rotating about their centre of mass only under their mutual gravitational attraction. Let the stars have masses m and 2m and let their separation be l. Their time period of rotation about their centre of mass will be proportional to

The correct options are B l3/2 D m−1/2F=Gm(2m)l2=mω2(2l/3)or 3mGl3=ω2.T=2πω=2π√l33mg

A binary star is a system of two stars rotating about their centre of mass only under their mutual gravitational attraction. Let the stars have masses $m$ and $2 m$ and let their separation be $l$ . Their time period of rotation about their centre of mass will be proportional to

The correct options are
B $l^{3 / 2}$
D $m^{- 1 / 2}$
$F = G \frac{m (2 m)}{l^{2}} = m ω^{2} (2 l / 3)$
or $\frac{3 m G}{l^{3}} = ω^{2} . T = \frac{2 π}{ω} = 2 π \sqrt{\frac{l^{3}}{3 m g}}$