An artificial satellite is moving in a circular orbit around the earth, with a speed which is equal to half the magnitude of the escape velocity from the earth. What is the height of the satellite above the surface of the earth ?

Options

A. 2 R
B. R
C. `(R )/(2)`
D. `(R )/(4)`

Answer

B

Explanation

It is given that `v_(0)=(1)/(2)v_(e )`
`therefore ((GM)/(R+h))=(1)/(2)sqrt((2GM)/(R ))`
`therefore (GM)/(R+h)=(1)/(4).(2GM)/(R )=(GM)/(2R)`
`therefore 2R=R+h " " therefore h = R`