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A space ship of mass 2 \times 10^{4} \mathrm{~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=10 \mathrm{~m} / \mathrm{s}^{2}$ and radius of earth $=6400 \mathrm{~km} ):

Option: 1

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


Option: 2

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


Option: 3

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


Option: 4

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


Answers (1)

best_answer

\Delta \mathrm{V}=\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}}(\sqrt{2}-1)
=\sqrt{\frac{\mathrm{GM}}{\mathrm{R}^{2}} \times \mathrm{R}}(\sqrt{2}-1)
=\sqrt{\mathrm{gR}}(\sqrt{2}-1)=8000(\sqrt{2}-1) \mathrm{ms}^{-1}
=8(\sqrt{2}-1) \mathrm{kms}^{-1}

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Pankaj

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