Gravitation Question 242

Question: The orbital velocity of an artificial satellite in a circular orbit just above the earth’s surface is v. For a satellite orbiting at an altitude of half of the earth’s radius, the orbital velocity is [MNR 1994]

Options:

A) $ [\frac{3}{2}v] $

B) $ [\sqrt{\frac{3}{2}},v] $

C) $ [\sqrt{\frac{2}{3}},v] $

D) $ [\frac{2}{3},v] $

Show Answer

Answer:

Correct Answer: C

Solution:

$ [v=\sqrt{\frac{GM}{R+h}}] $ For first satellite $ [h=0] $ , $ [v_{1}=\sqrt{\frac{GM}{R}}] $ For second satellite $ [h=\frac{R}{2}] $ , $ [v_{2}=\sqrt{\frac{2GM}{3R}}] $ $ [v_{2}=\sqrt{\frac{2}{3}}v_{1}=\sqrt{\frac{2}{3}}v] $



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