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Question #42055

Difficulty: 8/10 | 🟢 Free

The Question

A simple pendulum of length $L$ and a bob of mass $m$ carrying charge $q$ is initially at rest in the vertical position ( $\theta = 0$ ). A uniform horizontal electric field $E$ is suddenly switched on. The new equilibrium position of the pendulum makes a small angle $\theta_0$ with the vertical. The bob subsequently swings and reaches a maximum angular displacement $\theta_{max}$ from the vertical. Assuming small-angle approximations are valid, what is the angular velocity of the bob when its angular displacement from the vertical is $\theta = \frac{3}{4}\theta_{max}$ ?

Options

A.
$\frac{\sqrt{3}}{2} \theta_0 \sqrt{\frac{g}{L}}$
B.
$\frac{\sqrt{15}}{4} \theta_0 \sqrt{\frac{g}{L}}$
C.
$\frac{\sqrt{7}}{2} \theta_0 \sqrt{\frac{g}{L}}$
D.
$\frac{\sqrt{7}}{4} \theta_0 \sqrt{\frac{g}{L}}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Turning Point Identification|Simple Pendulum Small Angle Approximation|Oscillations

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to identify the correct turning point and reference frame for a pendulum subjected to a constant horizontal force.

The primary trap lies in failing to recognize that the new equilibrium position is shifted to $\theta_0$ , making the motion simple harmonic about this new tilted axis, not the vertical.

Consequently, the true turning point (maximum displacement) is $2\theta_0$ , not $\theta_0$ .

Common mistakes include assuming the equilibrium position is the turning point (yielding Option B), or correctly identifying the turning point but incorrectly calculating the velocity by assuming SHM about the vertical axis (yielding Options C and D).

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Motion in a Straight Line - Class 11 Part 1
Concept	Turning Point Identification
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free