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Question

Physics Question on Escape Speed

For a satellite moving in an orbit around the earth, the ratio of kinetic to potential energy is:

A

1:02

B

2:01

C

1:01

D

4:01

Answer

1:02

Explanation

Solution

Key Idea: The potential energy of satellite is twice its kinetic energy but opposite in sign. Potential energy, U=−GMemReor∣U∣=GMemReU=-\frac{G{{M}_{e}}m}{{{R}_{e}}}or|U|=\frac{G{{M}_{e}}m}{{{R}_{e}}} Kinetic energy, K=12GMemReK=\frac{1}{2}\frac{G{{M}_{e}}m}{{{R}_{e}}} Thus, K∣U∣=12GMemRe×ReGMem=12\frac{K}{|U|}=\frac{1}{2}\frac{G{{M}_{e}}m}{{{R}_{e}}}\times \frac{{{R}_{e}}}{G{{M}_{e}}m}=\frac{1}{2}