Question 169 of 223

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)

A$2.5 R$B$3 R$C$4 R$D$6 R$

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Answer: (D) $6 R$

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