How is it that upon doubling the separation between two masses, the force of attraction b/w them is reduced to one fourth??

Asked by Mala | 20th Jul, 2017, 08:17: PM

Expert Answer:

-Applying the Universal Law of Gravitation, the force of attraction between two masses is given by
begin mathsize 12px style straight F equals GMm over straight r squared end style
-Where, G is the universal gravitational constant, M is the mass of the Earth, m is the mass of any given body and r is the distance between the bodie and the Earth in this case.
-Now its begin mathsize 12px style straight F equals GMm 1 over straight r squared end style, so if the distance is doubled, r becomes 2r and the equation for F becomes begin mathsize 12px style straight F equals GMm 1 over open parentheses 2 straight r close parentheses squared equals 1 fourth open parentheses GMm over straight r squared close parentheses equals 1 fourth straight F end style.
-Therefore, on doubling the separation between two masses, the force of attraction b/w them is reduced to one fourth.
 
Hope this helped :)

Answered by Abhijeet Mishra | 21st Jul, 2017, 10:07: AM

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