Karan and Arjun are two friends of mass `m_(1)` and `m_(2)` respectively, separated by a distance d.
What would happen to the force between them if
(i) Massof Arjun is doubled.
(ii) Mass of both Karan and Arjun is doubled.
(iii) Distance between them is doubled.
(iv) Value of G doubled.

Explanation

The force between Karan and Arjun is
`F=(Gm_(1)m_(2))/(d^(2))`…….i
(i) If `m_(2)` is doubled.
`F^(1)=(Gm_(1)(2m_(2)))/(d^(2))=(2(Gm_(1)m_(2)))/(d^(2))`
`F^(1)=2F`……..[from (i)]
Force becomes double.
(i) If `m_(1)` and `m_(2)` are doubled.
`F^(1)-(G(2m_(1))(2m_(2)))/(d^(2))=(4(Gm_(1)m_(2)))/(d^(2))`
`F^(1)=4F` [from (i)]
Force becomes 4 times.
(iii) If d is doubled.
`F^(1)=(Gm_(1)m_(2))/((2d)^(2))=1/4((Gm_(1)m_(2)))/(d^(2))`
`F^(1)=1/4F`.....[from (i)]
Force becomes one forth.
(iv) If G is doubled.
`F^(1)=(2Gm_(1)m_(2))/(d^(2))=2F`....[from (i)]
Force is doubled.