The mass and the diameter of a planet are three times the...

The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is

2 \mathrm{~s}

. The period of oscillation of the same pendulum on the planet would be:

Options

A $\frac{\sqrt{3}}{2} \mathrm{~s}$
B $\frac{2}{\sqrt{3}} \mathrm{~s}$
C $\frac{3}{2} s$
D $2 \sqrt{3}$ s

Correct answer

D. $2 \sqrt{3}$ s

Step-by-step solution

Acceleration due to gravity

\mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}^{2}}

\frac{g_{p}}{g_{e}}=\frac{M_{p}}{M_{e}}

\left(\frac{R_{e}}{R_{p}}\right)^{2}=3

\left(\frac{1}{3}\right)^{2}=\frac{1}{3}

Also

\mathrm{T} \propto \frac{1}{\sqrt{\mathrm{g}}} \Rightarrow \frac{\mathrm{T}_{\mathrm{p}}}{\mathrm{T}_{\mathrm{e}}}=\sqrt{\frac{\mathrm{g}_{\mathrm{e}}}{\mathrm{g}_{\mathrm{p}}}}=\sqrt{3}

\Rightarrow \mathrm{T}_{\mathrm{p}}=2 \sqrt{3} \mathrm{~s}

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