Two simple pendulums having lengths I 1 and I 2 with negligible string mass undergo angular displacements θ 1 and θ 2 , from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?

Physics · Simple Harmonic Motion

JEE Main 2025 — 4 April, Morning Shift — Question 56

Two simple pendulums having lengths $I_{1}$ and $I_{2}$ with negligible string mass undergo angular displacements $\theta_{1}$ and $\theta_{2}$ , from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?

Option A:
$\theta_{1} I_{1}^{2}=\theta_{2} I_{2}^{2}$
Option B:
$\theta_{1} I_{2}^{2}=\theta_{2} I_{1}^{2}$
Option C:
$\theta_{1} I_{1}=\theta_{2} I_{2}$
Option D:
$\theta_{1} I_{2}=\theta_{2} I_{1}$
Correct

Answer: D

Step-by-step solution

$\theta=\theta_{0} \sin (\omega t+\phi)$

\begin{gathered} \frac{d^{2} \theta}{d t^{2}} =-\theta_{0} \omega^{2} \sin (\omega t+\phi) =-\theta_{0} \cdot \frac{g}{l} \sin (\omega t+\phi) \frac{\theta_{1}}{I_{1}}=\frac{\theta_{2}}{I_{2}} \theta_{1} I_{2}=\theta_{2} I_{1} \end{gathered}

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 4 April, Morning Shift
Subject: Physics
Chapter: Simple Harmonic Motion
Topic: Simple Pendulum and Angular SHM