The ratio of frequencies of two pendulums is | vedclass

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(D) The frequency $n$ of a simple pendulum is given by the formula $n = \frac{1}{2\pi} \sqrt{\frac{g}{l}}$.This implies that $n \propto \frac{1}{\sqrt

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$9/4$

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(D) The frequency $n$ of a simple pendulum is given by the formula $n = \frac{1}{2\pi} \sqrt{\frac{g}{l}}$.This implies that $n \propto \frac{1}{\sqrt{l}}$.Given the ratio of frequencies $\frac{n_1}{n_2} = \frac{2}{3}$.Since $\frac{n_1}{n_2} = \sqrt{\frac{l_2}{l_1}}$,we have $\frac{2}{3} = \sqrt{\frac{l_2}{l_1}}$.Squaring both sides,we get $\frac{4}{9} = \frac{l_2}{l_1}$.Therefore,the ratio of their lengths is $\frac{l_1}{l_2} = \frac{9}{4}$.

The ratio of frequencies of two pendulums is $2 : 3$. What is the ratio of their lengths?

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