The period of the pendulum in the Moon is 3.9 s
Explanation:
The period of a simple pendulum is given by the equation
[tex]T=2\pi \sqrt{\frac{L}{g}}[/tex] (1)
where
L is the length of the pendulum
g is the acceleration due to gravity
Here we have a pendulum whose period on Earth is
[tex]T_e = 1.6 s[/tex]
where on Earth, the acceleration due to gravity is
[tex]g_e = 9.8 m/s^2[/tex]
So eq.(1) can be written as
[tex]T_e = 2\pi \sqrt{\frac{L}{g_e}}[/tex] (2)
When the same pendulum is moved to the Moon, its length does not change, so its period on the Moon is given by
[tex]T_m = 2\pi \sqrt{\frac{L}{g_m}}[/tex] (3)
where
[tex]g_m = \frac{1}{6}g_e[/tex] is the acceleration due to gravity on the Moon (1/6 of that on the Earth)
Dividing eq.(3) by eq.(2), we get
[tex]\frac{T_m}{T_e}=\sqrt{\frac{g_e}{g_m}}=\sqrt{\frac{g_e}{\frac{1}{6}g_e}}=\sqrt{6}[/tex]
Therefore, the period of the pendulum on the moon is
[tex]T_m = \sqrt{6}T_e = \sqrt{6}(1.6)=3.9 s[/tex]
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