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  • A satellite is revolving round the earth in an orbit of radius with time period <img alt="\mathrm{T}"

A satellite is revolving round the earth in an orbit of radius \mathrm{r} with time period \mathrm{T}. If the satellite is revolving round the earth in an orbit of radius \mathrm{r+\Delta r(\Delta r<r)} with time period \mathrm{\mathrm{T}+\Delta \mathrm{T}(\Delta \mathrm{T}<<\mathrm{T})} then.
 

Option: 1

\frac{\Delta \mathrm{T}}{\mathrm{T}}=\frac{3}{2} \frac{\Delta \mathrm{r}}{\mathrm{r}}

 


Option: 2

\mathrm{\frac{\Delta \mathrm{T}}{\mathrm{T}}=\frac{2}{3} \frac{\Delta \mathrm{r}}{\mathrm{r}}}
 


Option: 3

\mathrm{\frac{\Delta T}{T}=\frac{\Delta r}{r}}
 


Option: 4

\mathrm{\frac{\Delta \mathrm{T}}{\mathrm{T}}=-\frac{\Delta \mathrm{r}}{\mathrm{r}}}


Answers (1)

best_answer

Since, \mathrm{\mathrm{T}^2=\mathrm{kr}^3}

\mathrm{ \Rightarrow 2 \frac{\Delta \mathrm{T}}{\mathrm{T}}=3 \frac{\Delta \mathrm{r}}{\mathrm{r}} }

\mathrm{ \Rightarrow \frac{\Delta \mathrm{T}}{\mathrm{T}}=\frac{3}{2} \frac{\Delta \mathrm{r}}{\mathrm{r}}}

Hence option 1 is correct.



 

Posted by

Gunjita

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