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Two small satellites moves in circular orbits around the earth, at distances r and \mathrm{r+\Delta r}r from the centre of earth. Their time periods of rotations are T and \mathrm{T+\Delta T} \mathrm{(\Delta r \ll r, \Delta T<<T) \text {. Then }}

Option: 1

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


Option: 2

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


Option: 3

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


Option: 4

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


Answers (1)

\mathrm{\begin{aligned} & \mathrm{T}^2 \propto \mathrm{r}^3 \text { or } \mathrm{T}^2=\mathrm{cr}^3 \\ & \Rightarrow 2 \mathrm{~T} \Delta \mathrm{T}=3 \mathrm{cr}^2 \Delta \mathrm{r} \end{aligned}}

On dividing

\mathrm{\begin{aligned} & \frac{2 \mathrm{~T} \Delta \mathrm{T}}{\mathrm{T}^2}=\frac{3 \mathrm{cr}^2 \Delta \mathrm{r}}{\mathrm{cr}^3} \\ & \Rightarrow \Delta \mathrm{T}=\frac{3}{2} \mathrm{~T} \frac{\Delta \mathrm{r}}{\mathrm{r}} \end{aligned}}

Hence (B) is correct.

Posted by

Sumit Saini

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