A) \[7:8\]
B) \[8:7\]
C) \[49:64\]
D) \[64:49\]
Correct Answer: D
Solution :
The frequency of oscillation of pendulum of length l, is given by \[n=\frac{1}{2\pi }\sqrt{\frac{g}{l}}\] Given, \[{{n}_{1}}:{{n}_{2}}=7:8,\] then \[\frac{{{n}_{1}}}{{{n}_{2}}}=\sqrt{\frac{{{l}_{2}}}{{{l}_{1}}}}\] \[\Rightarrow \] \[\frac{7}{8}=\sqrt{\frac{{{l}_{2}}}{{{l}_{1}}}}\] On squaring \[\Rightarrow \] \[\frac{{{l}_{1}}}{{{l}_{2}}}=\frac{64}{49}\]
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