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derive the ex...

Question

derive the expression for acceleration due to gravity.

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Solution

$W e k n o w N e w t o n' s l a w o f g r a v i t a t i o n a l f o c e o f a t t r a c t i o n o f e a r t h o n m a s s m i s g i v e n b y, F = G \frac{M m}{R^{2}}, w h e r e G, M a n d R a r e u n i v e r s a l c o n s \tan t o f g r a v i t y, m a s s o f t h e e a r t h a n d r a d i u s o f t h e e a r t h r e s p e c t i v e l y . T h e w e i g h t o f t h e b o d y o f m a s s m i s, W = m g b u t t h e s e t w o f o r c e s a r e t h e s a m e, s o F = W a n d m g = G \frac{M m}{R^{2}} o r g = G \frac{M}{R^{2}} . T h i s i s t h e r e q u i r e d e x p r e s s i o n f o r g r a v i t y .$

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