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.
  1. $\frac{E}{4}$
  2. E
  3. $\frac{\mathrm{E}}{2}$
  4. 2 E

Solution

By conservation of energy, $\begin{aligned} & \mathrm{U}_{\mathrm{i}}+\mathrm{K}_{\mathrm{i}}+\Delta \mathrm{E}=\mathrm{U}_{\infty}+\mathrm{K}_{\infty} \\ & \Rightarrow-2 \mathrm{~K}_{\mathrm{i}}+\mathrm{K}_{\mathrm{i}}+\Delta \mathrm{E}=0 \\ & \therefore \Delta \mathrm{E}=\mathrm{K}_{\mathrm{i}}=\mathrm{E} \end{aligned}$

Asked in: AP EAMCET 2024 (22 May Shift 1)

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