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Question

A body of mass m kg. starts falling from a point 2R above the earth’s surface. Its kinetic energy when it has fallen to a point ‘R’ above the eart’s surface [R – Radius of earth, M – Mass of earth, G – Gravitational constant]


A

12GMmR

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B

16GMmR

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C

23GMmR

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D

13GMmR

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Solution

The correct option is B

16GMmR


When body starts falling toward earth’s surface its potential energy decreases so kinetic energy increases.

Increase in kinetic energy = Decrease in potential energy

Final kinetic energy – Initial kinetic energy = Initial potential energy – Final potential energy

Final kinetic energy - 0 = (GMmr1)(GMmr2)

Final kinetic energy =(GMmR+h1)(GMmR+h2)=(GMmR+2R)(GMmR+R)=GMm3R+GMm2R=16GMmR


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