A simple pendulum having length l and mass 'm' is suspended between two plates having uniform electric field 'E' as shown in figure. The bob is given a charge q . The time period 'T' of its vibration is

Step-by-step solution

The forces acting on the bob of the pendulum are the gravitational force mg acting downwards and the electrostatic force qE acting downwards (since the electric field E is directed downwards and the charge q is assumed positive). The net downward force on the bob is F_ net = mg + qE . The effective acceleration due to gravity is g_ eff = F_ net m = g + qE m . The time period of a simple pendulum is given by T = 2 l g_ eff . Substituting the value of g_ eff , we get T = 2 l g + qE m . Answer: 2 l g + Eq m