Two pendulums begin to swing simultaneously. If the ratio of the frequency of oscillations of the two is 7: 8, then the ratio of lengths of the two pendulums will be

7:8

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8:7

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49:64

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64:49

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Solution

The correct option is D 64:49
Suppose at $t = 0$ , pendulums beings to given ro swing simultaneously.

Hence they will again swing simultaneously
if $n_{1} T_{1} = n_{2} T_{2}$

$\Rightarrow \frac{n_{1}}{n_{2}} = \frac{T_{2}}{T_{1}} = \sqrt{\frac{l_{2}}{l_{1}}}$

$\Rightarrow \frac{l_{1}}{l_{2}} = {(\frac{n_{2}}{n_{1}})}^{2} = {(\frac{8}{7})}^{2} = \frac{64}{49}$

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