First slide

Simple harmonic motion

Question

The periods of a pendulum on two planets are in the ratio 3:4, the acceleration due to gravity on them are in the ratio

Moderate

A

9:16
B

3:4
C

4:3
D

16:9

Solution

$T = 2 π \sqrt{\frac{l}{g}} \Rightarrow \frac{T_{1}}{T_{2}} = \sqrt{\frac{g_{2}}{g_{1}}} \Rightarrow {[\frac{3}{4}]}^{2} = \frac{g_{2}}{g_{1}} \Rightarrow \frac{g_{1}}{g_{2}} = \frac{16}{9}$

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