A body revolved around the sun $27$ times faster then the earth what is the ratio of their radii
A body revolved around the sun $27$ times faster then the earth what is the ratio of their radii
$ \frac{1}{3}$
$ \frac{1}{9}$
$ \frac{1}{27}$
$ \frac{1}{4}$
A body revolved around the sun $27$ times faster then the earth what is the ratio of their radii
${\omega _{{\rm{body}}}} = 27{\omega _{{\rm{earth}}}}$
${T^2} \propto {r^3} $
$\Rightarrow {\omega ^2} \propto \frac{1}{{{r^3}}}$
$\Rightarrow \omega \propto \frac{1}{{{r^{3/2}}}}$
$r \propto \frac{1}{{{\omega ^{2/3}}}}$
$\frac{{{r_{{\rm{body}}}}}}{{{r_{{\rm{earth}}}}}} = {\left( {\frac{{{\omega _{{\rm{earth}}}}}}{{{\omega _{{\rm{body}}}}}}} \right)^{2/3}}$
$ = {\left( {\frac{1}{{27}}} \right)^{2/3}} = \frac{1}{9}$
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