Electrostatics 5 Question 3

3. A simple pendulum of length L is placed between the plates of a parallel plate capacitor having electric field E, as shown in figure. Its bob has mass m and charge q. The time period of the pendulum is given by

(Main 2019, 10 April II)

(a) 2πLg2+qEm

(b) 2πLg2q2E2m2

(c) 2πLg+qEm

(d) 2πLgqEm

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Answer:

Correct Answer: 3. (a)

Solution:

  1. When pendulum is oscillating between capacitor plates, it is subjected to two forces;

(i) Weight downwards =mg

(ii) Electrostatic force acting horizontally =qE

So, net acceleration of pendulum bob is resultant of accelerations produced by these two perpendicular forces.

Net acceleration is, anet =a12+a22=g2+qE2m

So, time period of oscillations of pendulum is

T=2πlanet=2πLg2+qEm



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