A particle carrying a charge of 2.0 10⁻⁴ C is positioned directly below the resting bob of a simple pendulum, at a separation of 10 cm . If the mass of the bob is 100 g , determine the charge that must be given to the bob such that the string becomes loose.

Step-by-step solution

For the string to become loose, the tension in the string must be zero. This happens when the upward electrostatic force balances the downward gravitational force. F_ e = mg 1 4 ₀ q₁ q₂ r^2 = mg Substituting the given values: 9 10^9 2.0 10⁻⁴ q₂ (0.1)^2 = 0.1 9.8 18 10^7 q₂ = 0.98 q₂ = 0.98 18 10^7 = 5.44 10⁻⁹ C The required charge is approximately 5.4 10⁻⁹ C .