question_answer

The orbital velocity of an artificial satellite in a circular orbit just above the earths surface is Vg. The orbital velocity of a satellite orbiting at an altitude of half of the radius, is

A)  \[\frac{3}{2}{{v}_{o}}\]                                

B)  \[\frac{2}{3}{{v}_{o}}\]

C)   \[\sqrt{\frac{2}{3}}{{v}_{o}}\]                  

D)  \[\sqrt{\frac{3}{2}}{{v}_{o}}\]

Correct Answer: C

Solution :

                 The orbital velocity of a satellite orbiting in a circular orbit at a height h above the earths surface is                 where R is radius of earth, G the gravitational constant and Mg the mass of earth. Given,   \[h=\frac{R}{2}\] \[\therefore \]  \[v_{0}^{}=\sqrt{\frac{GM}{R+\frac{R}{2}}}\]                 \[=\sqrt{\frac{GM}{\frac{3}{2}{{R}_{e}}}}=\sqrt{\frac{2}{3}}.\,{{v}_{0}}\]