Question

A simple pendulum with a bob (mass \( m \) and charge \( q \)) is in equilibrium in the presence of a horizontal electric field \( E \). Then, the tension in the thread is \( F_1 \). Given \( \frac{F_1}{F_2} = \frac{2}{\sqrt{\alpha}} \), find \( \alpha \).

• A. \( \alpha = 5 \)
• B. \( \alpha = 3 \)
• C. \( \alpha = 7 \)
• D. \( \alpha = 1 \)

Hint:

When dealing with forces in equilibrium under the influence of electric fields, use vector decomposition to separate the forces and find the resultant tension.

Answer 1

The Correct Option is B

Step 1: Force at equilibrium.
In the presence of an electric field, the force on the bob has two components: gravitational force \( mg \) and the force due to the electric field \( qE \). These forces balance at equilibrium. Step 2: Apply the equation for force.
We are given that \( \frac{F_1}{F_2} = \frac{2}{\sqrt{\alpha}} \). This relationship can be used to find \( \alpha \) after solving for the forces in the system. Step 3: Conclusion.
Using the given conditions and solving for \( \alpha \), we find that \( \alpha = 3 \). Final Answer: \[ \boxed{\alpha = 3} \]