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Potential energy

A body of mas...

Question

A body of mass m is taken to a height kR from the surface of the earth very slowly, R being the radius of the earth. Find the change in gravitational Potential Energy in this process.

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Solution

$P o t e n t i a l e n e r g y a t t h e s u r f a c e o f t h e a r t h i s - \frac{G M m}{R} w h e r e R i s t h e r a d i u s o f t h e e a r t h M i s t h e m a s s o f t h e e a r t h m i s t h e m a s s o f t h e o b j e c t . P o t e n t i a l e n e r g y a t h e i g h t h = k R i s g i v e n b y : P E = - \frac{G M m}{K R} c h a n g e i n p o t e n t i a l e n e r g y = - \frac{G M m}{K R} + - \frac{G M m}{R} = \frac{G M m}{R} [1 - \frac{1}{k}] = \frac{G M m}{R} [\frac{1 - k}{k}]$

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