A) \[\infty \]
B) \[\sqrt{\frac{3}{5}}T\]
C) \[\sqrt{\frac{5}{3}}T\]
D) \[\frac{T}{\sqrt{2}}\]
Correct Answer: D
Solution :
Time period of simple pendulum is given by \[T=2\pi \sqrt{\frac{l}{g}}\] ...(i) and \[T=2\pi \sqrt{\frac{l}{g+g}}\] \[({{g}_{eff}}=g+g)\] \[\Rightarrow \] \[T=2\pi \sqrt{\frac{l}{2g}}\] \[\Rightarrow \] \[T=2\pi \sqrt{\frac{l}{g}}\frac{1}{\sqrt{2}}\] [from Eq.(i)] \[\therefore \] \[T=\frac{R}{\sqrt{2}}\]
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