The gravitational force between two object is F. How will this force change when
(i)distance between them is reduced to half?
(ii) the mass of each object is quadrupled?

Explanation

(i) According to Newton's law of gravitation , gravitational force F between two object distance r apart is
`F prop(1)/(r^2)`
When distance between them is reduced to half,i.e.,`r'= r/(2')`, the force, `F' prop (1)/(r^(2))`
Thus,`(F')/(F)=(r^(2))/(r'^(2)) = (r^(2))/((r//2)^2)= 4 or F' = 4F`
(ii) Again according to newton's law of gravitation, the gravitational force F between two objects of masses `m_(1)` and `m_(2)` is
`F prop m_(1) m_(2)`
When mass of each object is quadrupled,
`m'_(1) = 4m_(1)` and `m'_(2) = 4m_(2)`
The force, `F' prop m'_(1) m'_(2)`
Thus, `(F')/(F)= (m'_(1)m'_(2))/(m_(1)m_(2))=((4m_(1))(4m_(2)))/(m_(1)m_(2)) = 16` or `F' = 16F`