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  4. A particle falls from infinity to the earth. Its velocity on reaching earth of radius R is:

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Q. A particle falls from infinity to the earth. Its velocity on reaching earth of radius R is:

JIPMERJIPMER 2002Work, Energy and Power

Solution:

At infinity, potential energy of the particle is zero. When it approaches to earth, its potential energy $ =-\,mgR. $ . This difference in potential energy $ mgR=\frac{1}{2}m{{\upsilon }^{2}} $ So, $ \upsilon =\sqrt{2Rg} $