Question

An artificial satellite is moving around earth in a circular orbit with speed equal to one fourth the escape speed of a body from the surface of earth. The height of satellite above earth's surface is (R is radius of earth)

• A. 3R
• B. 5R
• C. 7R
• D. 8R

Answer 1

The correct option is C 7R

Escape velocity $=\sqrt{2gR}$

Speed of satellite=$\frac{\sqrt{2gR}}{4}$

By force balance,

$\frac{GMm}{x^2}=\frac{m(\frac{\sqrt{2gR}}{4}{)}^2}{x}$

$x=\frac{GM}{2gR}\times 16=8\frac{GM}{gR}=8R$

Height of satellite above earth's surface is $8R-R=7R$