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



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