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

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

J & K CETJ & K CET 2005Gravitation

Solution:

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\% $