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Potential Energy

A body is rel...

Question

A body is released at a distance r(r>R) from the centre of the earth. What is the velocity of the body when it strikes the surface of the earth?

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Solution

Dear student,

$P o t e n t i a l E n e r g y U a t r = - \frac{G M_{e} m}{r} P o t e n t i a l e n e r g y a t R_{e}, U = - \frac{G M_{e} m}{R_{e}} T h e c h a n g e i n U f r o m r t o R_{e} i s e q u a l t o l o s s o f p o t e n t i a l e n e r g y d u e t o f a l l = - G M_{e} m (\frac{1}{R_{e}} - \frac{1}{r}) S o \frac{1}{2} m v^{2} = - G M_{e} m (\frac{1}{R_{e}} - \frac{1}{r}) V^{2} = - 2 G M_{e} (\frac{1}{R_{e}} - \frac{1}{r})$

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