Gravitation Question 346
Question: An artificial satellite is first taken to a height equal to half the radius of earth. Assume that it is at rest on the earth’s surface initially and that it is at rest at this height. Let $ [E_{1}] $ be the energy required. It is then given the appropriate orbital speed such that it goes in a circular orbit at that height. Let E be the energy required. The ratio $ [\frac{E_{1}}{E_{2}}] $ is
Options:
A) 4:1
B) 3:1
C) 1:1
D) 1:2
Show Answer
Answer:
Correct Answer: C
Solution:
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$ [E_{1}=-\frac{GM_{e}m}{{R_{e}}+\frac{{R_{e}}}{2}}\left( -\frac{GM_{e}m}{{R_{e}}} \right)=\frac{GM_{e}m}{3{R_{e}}}] $ $ [E_{2}=\frac{1}{2}mv_{0}^{2}=\frac{1}{2}m.\frac{GM_{e}}{{R_{e}}+\frac{{R_{e}}}{2}}=\frac{GM_{e}m}{3{R_{e}}}] $
$ [\therefore \frac{E_{1}}{E_{2}}=1:1] $
