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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