A) 7 : 8
B) 8 : 7
C) 49 : 64
D) 64 : 49
Correct Answer: B
Solution :
Suppose at \[t=0\], pendulums begins to swing simultaneously. Hence, they will again swing simultaneously if \[{{n}_{1}}{{T}_{1}}={{n}_{2}}{{T}_{2}}\] \[\Rightarrow \] \[\frac{{{n}_{1}}}{{{n}_{2}}}=\frac{{{T}_{2}}}{{{T}_{1}}}=\sqrt{\frac{{{l}_{2}}}{{{l}_{1}}}}\Rightarrow \frac{{{l}_{1}}}{{{l}_{2}}}={{\left( \frac{{{n}_{2}}}{{{n}_{1}}} \right)}^{2}}={{\left( \frac{8}{7} \right)}^{2}}=\frac{64}{49}\]
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