Answer
The charge on the ball bearing is -10 nC.
Work Step by Step
Let $q_1$ be the charge on the glass bead. Let $q_2$ be the charge on the ball bearing. We can find the magnitude of $q_2$.
$F = \frac{k~q_1~q_2}{r^2}$
$q_2 = \frac{F~r^2}{k~q_1}$
$q_2 = \frac{(0.018~N)(0.010~m)^2}{(9.0\times 10^9~N~m^2/C^2)(20\times 10^{-9}~C)}$
$q_2 = 10~nC$
The magnitude of the charge on the ball bearing is 10 nC. Since the ball bearing feels a downward force, the charge on the ball bearing must be negative. The charge on the ball bearing is -10 nC.
