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  • Two satellite (I) and (II) are moving round a planet in circular orbit having radii <img alt="\mathrm{\mathrm{R} \: and\: 3 R}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Cm

Two satellite (I) and (II) are moving round a planet in circular orbit having radii \mathrm{\mathrm{R} \: and\: 3 R} respectively, if the speed of satellite \mathrm{(I)}  is \mathrm{v} the speed of satellite \mathrm{B} will be
 

Option: 1

\mathrm{\quad v / 3}

 


Option: 2

\mathrm{\frac{\mathrm{v}}{\sqrt{3}}}
 


Option: 3

\mathrm{3 v}
 


Option: 4

Data insufficient


Answers (1)

best_answer

\mathrm{ \mathrm{T}=2 \pi \mathrm{r} / \mathrm{v} }

\mathrm{ \mathrm{T}_1=2 \pi \mathrm{R} / \mathrm{v}_1 \text { and } \mathrm{T}_2=2 \pi 3 \mathrm{R} / \mathrm{v}_2 }

\mathrm{ \frac{\mathrm{T}_1}{\mathrm{~T}_2}=\frac{1}{3}\left(\frac{\mathrm{v}_2}{\mathrm{v}_1}\right) }

\mathrm{ \left(\frac{\mathrm{T}_1}{\mathrm{~T}_2}\right)^2=\frac{1}{9}\left(\frac{\mathrm{v}_2}{\mathrm{v}_1}\right)^2}

But by Kepler's third law \mathrm{\frac{\mathrm{T}_1^2}{\mathrm{~T}_2^2}=\left(\frac{\mathrm{R}_1}{\mathrm{R}_2}\right)^3=\left(\frac{1}{3}\right)^3}

\mathrm{\left(\frac{1}{3}\right)^3=\frac{1}{9}\left(\frac{\mathrm{v}_2}{\mathrm{v}_1}\right)^2 \Rightarrow \quad \mathrm{V}_2=\frac{\mathrm{v}_1}{\sqrt{3}} }

Hence option 3 is correct.
 

Posted by

sudhir kumar

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