Gravitation - Result Question 47
50. For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is
[2005]
(a) $\frac{1}{2}$
(b) $\frac{1}{\sqrt{2}}$
(c) 2
(d) $\sqrt{2}$
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Answer:
Correct Answer: 50. (a)
Solution:
- (a) K.E. of satellite moving in an orbit around the earth is
$K=\frac{1}{2} m v^{2}=\frac{1}{2} m(\sqrt{\frac{G M}{r}})^{2}=\frac{G M m}{2 r}$
P.E. of satellite and earth system is
$U=\frac{G M m}{r} \Rightarrow \frac{K}{U}=\frac{\frac{G M m}{2 r}}{\frac{G M m}{r}}=\frac{1}{2}$
