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  4. A body of mass m is released from a height equal to the radius R of the earth. What will be the velocity of the body when it strikes the surface of the earth?

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Q. A body of mass m is released from a height equal to the radius R of the earth. What will be the velocity of the body when it strikes the surface of the earth?

CMC MedicalCMC Medical 2015

Solution:

From work-energy theorem, $ \frac{1}{2}m{{v}^{2}}=-\,GMm\left[ \frac{1}{2R}-\frac{1}{R} \right] $ $ \Rightarrow $ $ \frac{1}{2}m{{v}^{2}}=\frac{-\,GMm}{2R} $ $ \Rightarrow $ $ v=\sqrt{gR} $ $ \left( \because g=\frac{GM}{{{R}^{2}}} \right) $