Solution
= Solution
Set $dF=0$ in the relative <total differential> and use the two equal $1\%$ mass increases:
$$
0=0.01+0.01-2\frac{dr}{r}\quad\Longrightarrow\quad\boxed{\frac{dr}{r}=0.01.}
$$
Thus the separation must \b[increase by $1\%$]. In this special case the result is also exact: the <mass> product increases by $1.01^2$, and preserving the inverse-square <force> requires $r_{\rm new}^2=1.01^2r^2$, hence $r_{\rm new}=1.01r$.