If the distance between the two bodies is increased to two 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)`
`therefore (Gm_(1)m_(2))/(r^(2))=(GM_(1)M_(2))/(R^(2))`
`therefore (m_(2))/(r^(2))=(M_(2))/((2r)^(2))`
`m_(2)=(M_(2))/(4)`
`therefore 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.