How is the gravitational force exerted by an object on earth is equal to 1.63 X 10^-24 ? And explain why it isn't equal to the gravitational force exerted by the earth on the body in accordance with the Newton's Third law.

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Solution

$G r a v i t a t i o n a l f o r c e o f a t t r a c t i o n e x e r t e d = 1.63 \times 10^{- 24} N, m a s s o f e a r t h = 6 \times 10^{24} K g, g = 9.8 m s^{- 2} . A c c o r d i n g t o N e w t o n' s l a w o f a c t i o n r e a c t i o n, m g = M a, w h e r e a i s a c c e l e r a t i o n p r o d u c e d b y a m a s s m = 1 K g o n e a r t h . T h u s a = 1 \times g / M = \frac{9.8}{6 \times 10^{24}} = 1.63 \times 10^{- 24} m s^{- 2} . T h e r e f o r e t h i s a c c e l e r a t i o n i s e x t r e m l y s m a l l c o m p a r e d t o t h e a c c e l e r a r a t i o n d u e t o g r a v i t y o f e a r t h g = 9.8 m s^{- 2} . N e w t o n' s l a w o f a c t i o n r e a c t i o n h o l d s g o o d i n t h i s c a s e b e c a u s e w h e n w e f i n d, m g = M a i . e . 1 \times 9.8 = 6 \times 10^{24} \times 1.63 \times 10^{- 24} = 9.8 N . T h e o n l y d i f f e r e n c e i s t h e i n c a s e o f s i m p l e m a s s o f 1 K g w e c a n e x p e r i e n c e t h e a c c e l e r a t i o n o f 9.8 m s^{- 2} b u t n o t i n c a s e o f e a r t h t h e a c c e l e r a t i o n o f 1.63 \times 10^{- 24} m s^{- 2} .$

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