Gravitation Question 237
Question: The ratio of the K.E. required to be given to the satellite to escape earth’s gravitational field to the K.E. required to be given so that the satellite moves in a circular orbit just above earth atmosphere is[NCERT 1975]
Options:
A) One
B) Two
C) Half
D) Infinity
Show Answer
Answer:
Correct Answer: B
Solution:
K.E.required for satellite to escape from earth’s gravitational field
$ [\frac{1}{2}mv_{e}^{2}=\frac{1}{2}m{{\left( \sqrt{\frac{2GM}{R}} \right)}^{2}}=\frac{GMm}{R}] $
K.E. required for satellite to move in circular orbit
$ [\frac{1}{2}mv_{0}^{2}=\frac{1}{2}m{{\left( \sqrt{\frac{GM}{R}} \right)}^{2}}=\frac{GMm}{2R}] $
The ratio between these two energies = 2
