State universal law of gravitation.The gravitational force between two objects is 100N.How should the distance between the objects be changed so that the force between them becomes 50N.

According to Newton's Law of Gravitation the force of gravitation between two objects separated by a certain distance is given as

F = GmM / r2

100 = GmM/ r2

r2 = GmM/100

now for the second case

 

F' = GmM / r'2

50 = GmM / r'2

r'2 =  GmM / 50

or

r'2 = 2 r2 

thus,

 

r' = r√2

 

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