Question

In the pendulum formula , we use g = 9.8 m/s2 for the acceleration due to gravity on Earth. But what about on the Moon? If an astronaut on the surface of the moon swings a 1-meter long pendulum, and it has a period of 4.9 seconds, what is the acceleration due to gravity, g, on the moon?

Answer 1

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1.6 m/s^2

Answer 2

The acceleration due to gravity on the moon is 1.642 m/s².

Explanation:

Given : In the pendulum formula , we use g = 9.8 m/s2 for the acceleration due to gravity on Earth. If an astronaut on the surface of the moon swings a 1-meter long pendulum, and it has a period of 4.9 seconds.

To find : What is the acceleration due to gravity, g, on the moon?

Solution :

The pendulum formula is
`T=2\pi \sqrt{(L)/(g)}`

where, T is the time period,

L is the length of the pendulum,

g is the acceleration due to gravity

We have to find the value of g acceleration due to gravity on the moon.

The formula became,

`g'=((2\pi)/(T))^2* L`

Substitute T=4.9 seconds , L= 1 m

`g'=((2* 3.14)/(4.9))^2* 1`

`g'=((6.28)/(4.9))^2`

`g'=(39.4384)/(24.01)`

`g'=1.642`

The acceleration due to gravity on the moon is 1.642 m/s².