If the Mass of a planet is 7 times mass of Earth and radius is twice that if Earth,then what is the diffrence in acceleration due to gravity on earth and on that planet

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Solution

Dear Student,
$G r a v i t a t i o n f o r c e b e t w e e n t w o b o d i e s o f m a s s M a n d m s e p a r a t e d b y a d i s \tan c e R F = G \frac{M m}{R^{2}} a c c e l e r a t i o n d u e t o g r a v i t y, g = G \frac{M}{R^{2}} F o r e a r t h' s g r a v i t y, M = m a s s o f e a r t h, R = r a d i u s o f t h e e a r t h G i v e n, m a s s o f a p l a n e t, M_{p} = 7 M R a d i u s o f t h e p l a n e t, R_{p} = 2 R T h u s, a c c e l e r a t i o n d u e g r a v i t y o n t h a t p l a n e t : g' = G \frac{7 M}{{(2 R)}^{2}} = \frac{7}{4} G \frac{M}{R^{2}} = \frac{7}{4} g D i f f e r e n c e i n a c c e l e r a t i o n d u e t o g r a v i t y o n e a r t h a n d o n t h a t p l a n e t = g - \frac{7}{4} g = - \frac{3}{4} g T h e a c c e l e r a t i o n d u e t o g r a v i t y o f t h e p l a n e t i s \frac{3}{4} g l e s s t h a n t h a t o f e a r t h .$
Regards

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