Charged Spheres in Equilibrium

Two positive spheres carry 96 nC and 64 nC. Their centres are 0.080 m apart. The hanging sphere is on a 1.2 m thread. Find its mass.

1. Find the electric repulsion.
   $$F=\dfrac{Q_1Q_2}{4\pi\varepsilon_0r^2}$$
   $$F=8.6\times10^{-3}\ \mathrm{N}$$
2. Find the thread angle from the geometry.
   $$\theta=\sin^{-1}\left(\dfrac{0.080}{1.2}\right)=3.8^\circ$$
3. Resolve tension, or use the force triangle.
   $$mg=\dfrac{F}{\tan\theta}=0.13\ \mathrm{N}$$
4. Divide by gravitational field strength.
   $$m=\dfrac{0.13}{9.81}=0.013\ \mathrm{kg}$$