A simple pendulum of length L , mass m and electric charge q on its bob is oscillating with a time period T under uniform gravity which is in the - z direction. Upon applying a uniform electric field |E| n (where n is a unit vector in the plane of oscillation), the time period of the pendulum decreases. Which of the following statements is NOT correct?

Step-by-step solution

The time period of a simple pendulum is given by T = 2 L g_ eff . For the time period to decrease, the effective acceleration due to gravity g_ eff must be greater than g . The effective acceleration is given by g _ eff = g + F _e m = -g z + q|E| n m . If q is positive and n = z , the electric force is in the + z direction. The effective gravity is g _ eff = -(g - q|E| m ) z . Assuming the electric force is smaller than the weight, g_ eff If q is positive and n = - z , the electric force is in the - z direction. Th