Question

A satelite is revolving in a circular orbit at a height h above the surface of the earth of radius R. The speed of the satellite in its orbit is one-fourth the escape velocity from the surface of the earth. The relation between h and R is
A. `h=2R`
B. `h=3R`
C. `h=5R`
D. `h=7R`

Answer 1

Correct Answer - D
Solution : `v_(C) =1/4 v_(e)`
`sqrt((GM )/((R+h)))=1/4 sqrt((2Gm)/((R+h)))`
`(GM )/((R+h))=(1)/(16) xx(2Gm)/((R+h))`
`R+h =8(R)`
`R+h=8(R)`
`7R =h`