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# A spaceship is lanunched into a circular orbit close to the earth's surface. What additional velocity has now to be imparted to the space ship in the orbit to overcome the gravitational pull. (Radius of earth$= 6400 km,g=9.8 m/s^2$)

$(a)\;\sqrt 2 gR \quad (b)\;\sqrt {2gR} \quad (c)\;\sqrt {gR} \quad (d)\;(\sqrt 2-1) \sqrt {gR}$

Orbital speed of satallite
$V_0=\sqrt {gR}$
$v_e$= escape velocity $=\sqrt {2gR}$
$v_e-v_0=\sqrt {2gR}-\sqrt {gR}$
$\qquad= (\sqrt 2 -1)\sqrt {gR}$
Hence d is the correct answer.

edited Feb 17, 2014 by meena.p