Question

A geostationary satellite is revolving around the earth. To make it escape from gravitational field of earth, its velocity must be increased

• A. $100\%$
• B. $41.4\%$
• C. $50\%$
• D. $59.6\%$

Answer 1

Answer: (B)

$41.4\%$

Answer 2

Orbital velocit $v_o=\sqrt{gR_e}$
Escape velocity $v_e=\sqrt{2gR_e}$
where $R_e$ is radius of earth.
$\%$ increase $=\frac{v_e-v_o}{v_o}\times100$
$\%$ increase $=\frac{\sqrt{2gR_e}-\sqrt{gR_e}}{\sqrt{gR_e}}\times100$
$=(\sqrt2-1)\times100$
$=(1.414-1)\times100=41.4\%$