A) \[\sqrt{\frac{G{{M}_{e}}}{{{R}_{e}}}}\]
B) \[\sqrt{\frac{2\,G{{M}_{e}}}{{{R}_{e}}}}\]
C) \[\sqrt{\frac{2\,Gm}{{{R}_{e}}}}\]
D) \[\frac{G{{M}_{e}}}{R_{e}^{2}}\]
Correct Answer: B
Solution :
Key Idea: If an energy equal to the binding energy of sphere on earth's surface is given to it in form of kinetic energy, it escapes the gravitational field of earth. |
The binding energy of sphere of mass m (say) on the surface of earth kept at rest is . To escape it from earth's surface, this much energy in the form of kinetic energy is supplied to it. |
So, |
or escape velocity |
Here, radius of earth, mass of earth. |
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