If the distance between the two spherical bodies is increased to four times, then by how many times, the mass of one of the bodies to be changed to maintain the same gravitational force ?

Explanation

`F_(1) = (Gm_(1)m_(2))/(r^(2))`
and `F_(2)(GM_(1)M_(2))/(R_(2))`
Now , R = 2r
Let `m_(1)` remains unchanged so `m_(1) = M_(1)`
` :. " "(Gm_(1)m_(2))/(r^(2)) = (GM_(1)M_(2))/(R^(2))`
` :. (m_(2))/(r^(2)) = (M_(2))/((2r)^(2))`
`m_(2) = (M_(2))/4`
` :. M_(2)= 4m_(2)`
Hence , the mass of one of the bodies should be increased to four times so that the gravitational force remains the same .