Question

A pendulum bob of mass'm' and charge 'q' is suspended by a thread of length /. The pendulum is placed in a region of a uniform electric field E directed vertically upward. If the electrostatic force acting on the sphere is less than that of gravitational force, the period with which the pendulum oscillates is : (Assume small oscillation)

Answer 1

1) In the absence of the electric field the pendulum oscillates in the gravitational field.

Its time period is given by T = 2π√(l/g).

When the electric field is applied, the effective downward force on the bob now becomes

mg ± qE. The effective force per unit mass now becomes (mg ± qE)/m = (g ± qE/m)

The time period T' = 2π√{i/(g ± qE/m)}.

Note: q is the numerical value of the charge. - ve sign is to be taken when the charge is positive

and + ve sign is to be taken when the charge is negative.