A body revolved around the sun 27 times faste | vedclass

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Question

(b)${\omega _{{\rm{body}}}} = 27{\omega _{{\rm{earth}}}}$

${T^2} \propto {r^3} $

$\Rightarrow {\omega ^2} \propto \frac{1}{{{r^3}}}$

$\Righta

Vedclass · Accepted Answer

$ \frac{1}{9}$

Vedclass · Answer

(b)${\omega _{{\rm{body}}}} = 27{\omega _{{\rm{earth}}}}$

${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}$

A body revolved around the sun $27$ times faster then the earth what is the ratio of their radii

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