Question

A simple pendulum has a bob with mass \(m\) and charge \(q\). The pendulum string has negligible mass. When a uniform and horizontal electric field \( \vec{E} \) is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is _______.
(\( g \): acceleration due to gravity)

• A. \( \sqrt{m^2 g^2 - q^2 E^2} \)
• B. \( \sqrt{m^2 g^2 + q^2 E^2} \)
• C. \( mg + qE \)
• D. \( mg - qE \)

Hint:

When forces act perpendicular to each other, the resultant magnitude is obtained using Pythagoras theorem.

Answer 1

The Correct Option is B

Step 1: Identify forces acting on the bob.
The bob experiences: \[ \text{Gravitational force } = mg \text{ (vertically downward)}, \] \[ \text{Electric force } = qE \text{ (horizontally)}. \]
Step 2: Condition of equilibrium.
At equilibrium, the tension \(T\) balances the resultant of gravitational and electric forces. Thus, \[ T = \sqrt{(mg)^2 + (qE)^2}. \]
Final Answer: \[ \boxed{\sqrt{m^2 g^2 + q^2 E^2}} \]