A satellite moving round the earth in a circular orbit has kinetic energy ' $E$ '. Then, the minimum amount…
A satellite moving round the earth in a circular orbit has kinetic energy ' $E$ '. Then, the minimum amount of energy to be added so that it escapes from the earth.
$\frac{E}{4}$
E
$\frac{\mathrm{E}}{2}$
2 E
Solution
By conservation of energy,
$\begin{aligned}
& \mathrm{U}_{\mathrm{i}}+\mathrm{K}_{\mathrm{i}}+\Delta \mathrm{E}=\mathrm{U}_{\infty}+\mathrm{K}_{\infty} \\
& \Rightarrow-2 \mathrm{~K}_{\mathrm{i}}+\mathrm{K}_{\mathrm{i}}+\Delta \mathrm{E}=0 \\
& \therefore \Delta \mathrm{E}=\mathrm{K}_{\mathrm{i}}=\mathrm{E}
\end{aligned}$