How much work will be done in taking a 10 kg body from the surface of the earth to infinity?what will be the gravitational potential energy of the body on the surface of the earth?if this body falls from infinity to the earth ,what will be its velocity when striking the earth ?

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Solution

$G r a v i t a t i o n a l f o r c e b e t w e e n t h e o b j e c t a n d t h e e a r t h i s g i v e n b y : F = \frac{G M m}{r^{2}} w h e n o b j e c t i s t a k e n a t i n f i n i t y f r o m t h e s u r f a c e o f t h e e a r t h i s g i v e n b y : U = - \int_{R}^{\infty} F d r w h e r e R i s t h e r a d i u s o f t h e e a r t h U = - \int_{R}^{\infty} \frac{G M m}{r^{2}} d r o n i n t e g r a t i n g w e g e t U = \frac{- G M m}{R} W e k n o w e n e r g y o f t h e b o d y r e m a i n s c o n s \tan t t h e i r f o r c e p o t e n t i a l e n e g r y a t i n f i n t y w i l l c o n v e r t i n t o t h e k i n e t i c e n e r g y w h e n a n o b j e c t s t r i k e t o t h e e a r t h . \frac{1}{2} m v^{2} = \frac{G M m}{R} v = \sqrt{\frac{2 G M}{R}}$

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