If the distance between two masses is increased by a factor of 4, by what factor would the mass of one of them have to be altered to maintain the same gravitational force?

Answer

`16time s`

Explanation

According to Newton's law of gravitation, `F=(Gm_(1)m_(2))/r^(2)`
when r is changed to r' and `(m'_(1),m'_(2))` to `(m'_(1),m'_(2))` respectively, then new force, `F'=(Gm'_(1)m'(2))/r'^(2)`
As `F'=F, (Gm'_(1)m_(2))/r'^(2)=(Gm_(1)m_(2))/r^(2)`
Now, as `r' =4r, (m'_(1)m'_(2))/(4r)^(2)=m_(1)m_(2)/r^(2)` or `m'_(1)m'_(2)=16m_(1)m_(2)`
Thus,mass of one of the objects has to be increase to 16 times.