A) 1 s
B) 2 s
C) \[2\sqrt{2\,s}\]
D) \[\frac{1}{2\sqrt{2}}s\]
Correct Answer: C
Solution :
\[T=2\pi \sqrt{\frac{l}{g}}=2\pi \sqrt{\frac{l}{GM/{{R}^{2}}}}=2\pi \sqrt{\frac{I{{R}^{2}}}{GM}}\] \[T\propto \frac{R}{\sqrt{M}}\] \[\frac{T'}{T}=\frac{R'}{R}\sqrt{\frac{M}{M'}}\] \[=2.\frac{1}{\sqrt{2}}=\sqrt{2}\] \[T'=\sqrt{2}T=2\sqrt{2}s\]
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