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
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(d) Suppose at $t = 0$, pendulums begins to 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}}}}$
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}}}}$
$\Rightarrow \frac{{{l_1}}}{{{l_2}}} = {\left( {\frac{{{n_2}}}{{{n_1}}}} \right)^2} = {\left( {\frac{8}{7}} \right)^2} = \frac{{64}}{{49}}$
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