A) 11
B) 10
C) 21
D) 20
Correct Answer: B
Solution :
Let \[{{T}_{1}}\] and \[{{T}_{2}}\] are the time period of the two pendulums \[{{T}_{1}}=2\pi \sqrt{\frac{100}{g}}\] and \[{{T}_{2}}=2\pi \sqrt{\frac{121}{g}}\] \[({{T}_{1}}<{{T}_{2}}\] because \[{{l}_{1}}<{{l}_{2}})\]. Let at \[t=0\], they start swinging together. Since their time periods are different, the swinging will not be in unision always. Only when number of completed oscillation differs by an integer, the two pendulum will again begin to swing together. Let longer length pendulum complete n oscillation and shorter length pendulum complete (n+1) oscillation, for the unision swinging, then \[(n+1){{T}_{1}}=n{{T}_{2}}\] \[(n+1)\times 2\pi \sqrt{\frac{100}{g}}=n\times 2\pi \sqrt{\frac{121}{g}}\]\[\Rightarrow n=10\]
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