Question

A pendulum makes 20 oscillations in 4.0s on earth and 40 oscillation on planet X. What is the acceleration due to gravity on planet X?

Answer 1

Answer: 4g

Explanation:

Given

The time on earth is 4 s for 20 oscillations

i.e. time period for one oscillation is $\frac{4}{20}=\frac{1}{5}\ s=0.2\ s$

for planet X it is 40 oscillations in 4 s i.e.

time period is $\frac{4}{40}=0.1\ s$

The time period of a pendulum is given by

$T=2\pi\sqrt{\dfrac{L}{g}}$

where L=length of the pendulum

g=acceleration due to gravity

So, we can write the ratio of the time period of two pendulums as

$\frac{0.2}{0.1}=\dfrac{2\pi\sqrt{\frac{L}{g}}}{2\pi\sqrt{\frac{L}{g'}} }$

$2=\sqrt{\frac{g'}{g}}$

$\sqrt{g'}=2\sqrt{g}\\g'=4g$

i.e. 4 times the gravity of the earth