Question

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 $2s$. The period of oscillation of the same pendulum on the planet would be :

• A. $\frac{2}{\sqrt{3}} s$
• B. $2 \sqrt{3} s$
• C. $\frac{\sqrt{3}}{2} s$
• D. $\frac{3}{2} s $

Answer 1

The Correct Option is B

$\because g = \frac{GM}{R^{2}} $ $ \frac{g_{p}}{g_{e}} = \frac{M_{e}}{M_{e}} \left(\frac{R_{e}}{R_{p}}\right)^{2} = 3\left(\frac{1}{3}\right)^{2} = \frac{1}{3} $ Also $ T\propto\frac{1}{\sqrt{g}} $ $\Rightarrow \frac{T_{p}}{T_{e}} = \sqrt{\frac{g_{e}}{g_{p}}} = \sqrt{3} $ $\Rightarrow \frac{T_{p}}{T_{e}} = 2 \sqrt{3} s$