#### Answer

(a) New distance $r_{2}$ is less than 10 times of the original distance $r_{1}$
$ r_{2} =\sqrt10 r_{1}=3.162 r_{1}$
(b) new distance will be $ 94.868cm$

#### Work Step by Step

Let us assume two charges $q_{1}$ and $q_{2}$ are separated by a distance $r_{1}$. In this case magnitude of force between them will be
$F_{1}=k\frac{q_{1}\times q_{2}}{r_{1}^2}$ ........equation (1)
Now suppose the are now moved farther apart to a distance $r_{2}$,In this case suppose force between them is $F_{2}$ which is decreased by a factor of 10.
$F_{2}=k\frac{q_{1}\times q_{2}}{r_{2}^{2}}$ ........equation (2)
given that $F_{2}=\frac{1}{10}\times F_{1}$
putting values of $F_{2}$ and $F_{1}$ from equation(1) and (2) we will get
$k\frac{q_{1}\times q_{2}}{r_{2}^{2}}=\frac{1}{10}\times k\frac{q_{1}\times q_{2}}{r_{1}^2}$
it gives $r_{2}^{2}=10\times r_{1}^{2}$
or $ r_{2} =\sqrt10 r_{1}=3.162 r_{1}$....equation(3)
(b)
original distance $ r_{1} =30cm$
so new distance will be $ r_{2} =3.162 r_{1}=3.162\times 30cm r_{1}=94.868cm$