An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the earth. The height of the satellite above the surface of the earth is x R. Find the value of x.

Options

A. 2R
B. R/2
C. R
D. R/4

Answer

C

Explanation

Escape velocity `v_e = sqrt((2GM)/(R ))`
Orbital velocity , `v_0 = sqrt((GM)/(R+ h))`
Given than `v_0 = (v_e)/(2)`
` therefore sqrt((GM)/(R + h)) = 1/2 sqrt((2GM)/(R )) " or "(GM)/( R+ h) = 1/4 xx (2GM)/( R)`
On solving , we get h = R