Respuesta :
Answer:
The acceleration due to gravity on the moon is 1.642 m/s².
Step-by-step 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 [tex]T=2\pi \sqrt{\frac{L}{g}}[/tex]
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,
[tex]g'=(\frac{2\pi}{T})^2\times L[/tex]
Substitute T=4.9 seconds , L= 1 m
[tex]g'=(\frac{2\times 3.14}{4.9})^2\times 1[/tex]
[tex]g'=(\frac{6.28}{4.9})^2[/tex]
[tex]g'=\frac{39.4384}{24.01}[/tex]
[tex]g'=1.642[/tex]
The acceleration due to gravity on the moon is 1.642 m/s².
