A) \[\frac{9}{7}\]
B) \[\frac{7}{9}\]
C) \[\frac{49}{81}\]
D) \[\frac{81}{49}\]
Correct Answer: C
Solution :
\[{{T}_{1}}=\frac{t}{9}\]and \[{{T}_{2}}=\frac{t}{7}\] Time period \[T=2\pi \sqrt{\frac{l}{g}}\] \[\Rightarrow \] \[{{T}^{2}}=4{{\pi }^{2}}\frac{l}{g}\] \[\therefore \] \[\frac{{{l}_{1}}}{{{l}_{2}}}={{\left( \frac{{{T}_{1}}}{{{T}_{2}}} \right)}^{2}}\] \[={{\left( \frac{t/9}{t/7} \right)}^{2}}=\frac{49}{81}\]
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