Two simple pendulums having lengths l1 and l2 with negligible string mass undergo angular displacements θ1 and θ2, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?

(A) \theta_1 l_2^2=\theta_2 l_1^2

(C) \theta_1 l_1^2=\theta_2 l_2^2

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JEE Mains · Physics · STD 11 - Oscillations

JEE Mains 2025
Medium
MCQ

Two simple pendulums having lengths \(l_1\) and \(l_2\) 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?

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Answer & Solution

Correct Answer

(D) \(\theta_1 l_2=\theta_2 l_1\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \omega=\sqrt{\frac{\mathrm{g}}{\ell}} \\ & \alpha=-\omega^2 \theta \\ & \therefore \frac{\mathrm{~g}}{\ell_1} \theta_1=\frac{\mathrm{g}}{\ell_2} \theta_2 \\ & \Rightarrow \theta_1 \ell_2=\theta_2 \ell_2\end{aligned}\)

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