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] $
