Two identical pith balls are charged by rubbing against one another. They are suspended from a horizontal rod using two strings of length 20 cm each, with a separation of 5 cm between the suspension points. In equilibrium, the separation between the balls is 3 cm . Determine the mass of each ball and the tension in the strings. The charge on each ball has a magnitude of 2.0 10⁻⁸ C .

Step-by-step solution

When the two identical pith balls are rubbed against each other, they acquire equal and opposite charges, leading to an electrostatic force of attraction between them. The electrostatic force of attraction is given by Coulomb's law: F_e = 1 4 ₀ q^2 r^2 Substituting the given values: F_e = 9 10^9 (2.0 10⁻⁸)^2 (0.03)^2 = 9 10^9 4.0 10⁻¹⁶ 9 10⁻⁴ = 4.0 10⁻³ N Let be the angle made by each string with the vertical. The suspension points are 5 cm apart, and the balls are 3 cm apart in equilibrium. By symmetry, the horizo