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Physics

Mechanics

Easy

Question

A double star is a system of two stars of masses m and 2 m. rotating about their centre of mass only under their mutual gravitational attraction. If r is the separation between these two stars then their time period of rotation about their centre of mass will be proportional to

$r^{\frac{3}{2}}$
r
$m^{\frac{1}{2}}$
$m^{- \frac{1}{2}}$

The correct answers are: $r to the power of 3 over 2 end exponent$ , $m to the power of negative 1 half end exponent$

$r subscript 2 equals fraction numerator 2 m r over denominator m plus 2 m end fraction equals fraction numerator 2 r over denominator 3 end fraction$

$table attributes columnalign left end attributes row cell T subscript 2 superscript 2 equals fraction numerator 4 pi squared r subscript 2 superscript 3 over denominator G m end fraction rightwards double arrow T subscript 2 superscript 2 equals fraction numerator 32 pi squared r cubed over denominator 27 G m end fraction end cell row cell T subscript 2 proportional to r to the power of 3 over 2 end exponent text and end text T subscript 2 proportional to m to the power of negative 1 half end exponent end cell end table$

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