A space ship of mass $2 \times 10^{4} kg$ is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if g=10m/s² and radius of earth $= 6400 km$ ):

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$11.2 (\sqrt{2} - 1) km / s$

$7.4 (\sqrt{2} - 1) km / s$

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

$7.9 (\sqrt{2} - 1) km / s$

answer is A.

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Detailed Solution

$ϑ^{1} = ϑ_{e} - ϑ_{0}; ϑ_{0} = \sqrt{\frac{GM}{R}} = 8 km / s ϑ_{e} = \sqrt{\frac{2 GM}{R}} = 8 \sqrt{2} km / s ∴ ϑ^{1} = 8 (\sqrt{2} - 1) km / s$

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