JEE Mains · Physics · STD 11 - 13. oscillations
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?
- A \(\theta_1 l_2^2=\theta_2 l_1^2\)
- B \(\theta_1 l_1=\theta_2 l_2\)
- C \(\theta_1 l_1^2=\theta_2 l_2^2\)
- D \(\theta_1 l_2=\theta_2 l_1\)
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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