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(C) The orbital velocity of a satellite close to the Earth's surface is given by $v_{	ext{orbit}} = \sqrt{gR}$.Substituting the values: $v_{	ext{orb

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$8(\sqrt{2}-1) \, km/s$

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(C) The orbital velocity of a satellite close to the Earth's surface is given by $v_{	ext{orbit}} = \sqrt{gR}$.Substituting the values: $v_{	ext{orbit}} = \sqrt{10 	imes 6.4 	imes 10^6} = \sqrt{64 	imes 10^6} = 8000 \, m/s = 8 \, km/s$.The escape velocity from the Earth's surface is given by $v_{	ext{escape}} = \sqrt{2gR} = \sqrt{2} 	imes v_{	ext{orbit}}$.Substituting the value: $v_{	ext{escape}} = 8\sqrt{2} \, km/s$.The additional velocity required to overcome the gravitational pull is $\Delta v = v_{	ext{escape}} - v_{	ext{orbit}}$.$\Delta v = 8\sqrt{2} - 8 = 8(\sqrt{2}-1) \, km/s$.

$A$ spaceship of mass $2 \times 10^4 \, kg$ is launched into a circular orbit close to the Earth's surface. The additional velocity to be imparted to the spaceship in the orbit to overcome the gravitational pull will be $......$ (given $g = 10 \, m/s^2$ and radius of Earth $R = 6400 \, km$).

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