Two pitch balls each weighing 19.6 × 10^-4 kg are suspended from the same point 'O' by two silk threads each 1 m long. Balls hold identical charge and repel each other making angle 90° at point 'O' between threads. The magnitude of charge is :

2.06 × 10^-6 C

Angle made by thread with vertical line at point O is $45^o$

At Equilibrium condition :

Along Vertical Direction :$ Tcos 45^o = mg$

Along Horizontal Direction $ Tsin 45^o = \frac{1}{4\pi \epsilon_0} \frac{q^2}{r^2} =\frac{1}{4\pi \epsilon_0} \frac{q^2}{{\sqrt 2}^2} = \frac{q^2}{8\pi \epsilon_0}$

divide equation (1) and (2) we get,

$ tan45^o = \frac{q^2}{8\pi \epsilon_0 mg}$

$\Rightarrow q^2 = 8\pi \epsilon_0 mg = \frac{2}{9\times 10^9} \times 19.6\times 10^{-4}\times 9.8$

$ q = 2.06\times 10^{-6} C$