A satellite of $10^3 \mathrm{~kg}$ mass is revolving in circular orbit of radius $2 R$. If $\frac{10^4 R}{6} J$ energy is supplied to the satellite, it would revolve in a new circular orbit of radius (use $g=10 \mathrm{~m} / \mathrm{s}^2, R=$ radius of earth)

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Aicharya · Accepted Answer

$\begin{aligned} & 	ext { Total energy }=\frac{-\mathrm{GMm}}{2(2 \mathrm{R})} \ & 	ext { if energy }=\frac{10^4 \mathrm{R}}{6} 	ext { is added then } \ & \frac{-\mathrm{GMm}}{4 \mathrm{R}}+\frac{10^4 \mathrm{R}}{6}=\frac{-\mathrm{GMm}}{2 \mathrm{r}} \ & 	ext { where } \mathrm{r} 	ext { is new radius of revolving and } \mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}^2} \ & -\frac{\mathrm{mgR}}{4}+\frac{10^4 \mathrm{R}}{6}=-\frac{\mathrm{mgR}^2}{2 \mathrm{r}}\left(\mathrm{m}=10^3 \mathrm{~kg}ight) \ & -\frac{10^3 	imes 10 	imes \mathrm{R}}{4}+\frac{10^4 \mathrm{R}}{6}=-\frac{10^3 	imes 10 	imes \mathrm{R}^2}{2 \mathrm{r}} \ & -\frac{1}{4}+\frac{1}{6}=-\frac{\mathrm{R}}{2 \mathrm{r}} \ & \mathrm{r}=6 \mathrm{R}\end{aligned}$

A satellite of $10^3 \mathrm{~kg}$ mass is revolving in circular orbit of radius $2 R$. If $\frac{10^4 R}{6}…

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