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

Step-by-step explanation:

Given

The time on earth is 4 s for 20 oscillations

i.e. time period for one oscillation is
`(4)/(20)=(1)/(5)\ s=0.2\ s`

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

time period is
`(4)/(40)=0.1\ s`

The time period of a pendulum is given by

`T=2\pi\sqrt{(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

`(0.2)/(0.1)=\frac{2\pi\sqrt{(L)/(g)}}{2\pi\sqrt{(L)/(g')} }`

`2=\sqrt{(g')/(g)}`

`√(g')=2√(g)\\g'=4g`

i.e. 4 times the gravity of the earth