Two simple pendulums having lengths $l_1$ and $l_2$ with negligible string mass undergo angular displacements $ heta_1$ and $ heta_2$, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?

Question

Two simple pendulums having lengths $l_1$ and $l_2$ with negligible string mass undergo angular displacements $	heta_1$ and $	heta_2$, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?

Aicharya · Accepted Answer

$\begin{aligned} & \omega=\sqrt{\frac{\mathrm{g}}{\ell}} \ & \alpha=-\omega^2 	heta \ & 	herefore \frac{\mathrm{~g}}{\ell_1} 	heta_1=\frac{\mathrm{g}}{\ell_2} 	heta_2 \ & \Rightarrow 	heta_1 \ell_2=	heta_2 \ell_1\end{aligned}$

Two simple pendulums having lengths $l_1$ and $l_2$ with negligible string mass undergo angular…

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