Two simple pendulums having lengths l_1 and l | vedclass

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(D) For a simple pendulum,the angular acceleration $\alpha$ is given by the equation $\alpha = -\omega^2 	heta$,where $\omega^2 = \frac{g}{l}$.Since

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$	heta_1 l_2 = 	heta_2 l_1$

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(D) For a simple pendulum,the angular acceleration $\alpha$ is given by the equation $\alpha = -\omega^2 	heta$,where $\omega^2 = \frac{g}{l}$.Since the angular accelerations are equal in magnitude,we have $|\alpha_1| = |\alpha_2|$.Substituting the expression for $\alpha$,we get $\frac{g}{l_1} 	heta_1 = \frac{g}{l_2} 	heta_2$.Canceling the acceleration due to gravity $g$ from both sides,we obtain $\frac{	heta_1}{l_1} = \frac{	heta_2}{l_2}$.Rearranging the terms,we get $	heta_1 l_2 = 	heta_2 l_1$.

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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