First slide

Simple hormonic motion

Question

The mass and diameter of a planet are twice those of earth. The period of oscillation of pendulum on this planet will be (If it is a second's pendulum on earth)

Moderate

A

$\frac{1}{\sqrt{2}} \sec$
B

$2 \sqrt{2} \sec$
C

2 sec
D

$\frac{1}{2} \sec$

Solution

As we know $g = \frac{GM}{R^{2}}$
$\Rightarrow \frac{g_{earth}}{g_{planet}} = \frac{M_{e}}{M_{p}} \times \frac{R_{ρ}^{2}}{R_{e}^{2}} \Rightarrow \frac{g_{e}}{g_{p}} = \frac{2}{1}$
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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