A) \[\frac{1}{\sqrt{2}}\] sec
B) \[2\sqrt{2}\]sec
C) 2 sec
D) \[\frac{1}{2}\]sec
Correct Answer: B
Solution :
As we know \[g=\frac{GM}{{{R}^{2}}}\] \[\Rightarrow \] \[\frac{{{g}_{\text{earth}}}}{{{g}_{\text{planet}}}}=\frac{{{M}_{e}}}{{{M}_{p}}}\times \frac{R_{\rho }^{2}}{R_{e}^{2}}\Rightarrow \frac{{{g}_{e}}}{{{g}_{p}}}=\frac{2}{1}\] Also \[T\propto \frac{1}{\sqrt{g}}\Rightarrow \frac{{{T}_{e}}}{{{T}_{p}}}=\sqrt{\frac{{{g}_{p}}}{{{g}_{e}}}}\Rightarrow \frac{2}{{{T}_{p}}}=\sqrt{\frac{1}{2}}\] \[\Rightarrow \] \[{{T}_{p}}=2\sqrt{2}\,\sec \].
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