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

Options

A. h=2R
B. h=3R
C. h=5R
D. h=7R

Answer

D

Explanation

According to the question,
`v_(c)=(1)/(4)v_(e)`
`sqrt((GM)/((R+h)))=(1)/(4)sqrt((2GM)/(R))`
On taking square root both sides, we get
`rArr" "(GM)/(R+h)=(1)/(16)(2GM)/(R)`
`rArr" "(GM)/(R+h)=(GM)/(8R)`
`rArr" "R+h=8R`
`rArr" "h=8R-R`
`rArr" "h=7R`