A) \[2\sqrt{3}s\]
B) \[\frac{3}{2}s\]
C) \[\frac{2}{\sqrt{3}}s\]
D) \[\frac{\sqrt{3}}{2}s\]
Correct Answer: A
Solution :
Time period of a simple pendulum, \[T=2\pi \sqrt{\frac{l}{g}}\] \[{{g}_{p}}=\frac{G{{M}_{p}}}{R_{p}^{2}}=4\frac{G{{M}_{p}}}{D_{p}^{2}}=\frac{(4G{{M}_{E}})}{D_{E}^{2}}\times \frac{3}{{{3}^{2}}}\] \[\left( \because {{g}_{e}}=\frac{4G{{M}_{E}}}{D_{E}^{2}} \right)\] \[{{g}_{p}}=\frac{{{g}_{e}}}{3}\] \[\therefore \]\[\frac{{{T}_{e}}}{{{T}_{p}}}=\sqrt{\frac{{{g}_{p}}}{{{g}_{e}}}}=\frac{1}{\sqrt{3}},{{T}_{p}}=2\sqrt{3}s\] \[({{T}_{e}}=2s)\]
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