question_answer

  A satellite of mass\[m\]revolve around the earth of radius R at a bright\[x\]from its surface. If\[g\]is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellites is          [AIEEE 2004]

A) \[gx\]                

B)       \[\frac{gR}{R-x}\]

C)  \[\frac{g{{R}^{2}}}{R+x}\]   

D)      \[{{\left( \frac{g{{R}^{2}}}{R+x} \right)}^{1/2}}\]

Correct Answer: D

Solution :

[d] The gravitational force exerted on satellite at a heightis

where, mass of the earth.

Since, gravitational force provides the necessary centripetal force, so

(where,is orbital speed of satellite)