Respuesta :
Explanation:
It is given that,
Length of the simple pendulum, l = 36.9 cm = 0.369 m
If it takes 14.2 s to complete 10 oscillations, [tex]T=\dfrac{14.2}{10}=1.42\ s[/tex]
(a) The time period of the simple pendulum is given by :
[tex]T=2\pi\sqrt{\dfrac{l}{g}}[/tex]
[tex]g=\dfrac{4\pi^2l}{T^2}[/tex]
[tex]g=\dfrac{4\pi^2\times 0.369}{(1.42)^2}[/tex]
[tex]g=7.22\ m/s^2[/tex]
(b) On the surface of moon, [tex]g'=\dfrac{g}{6}[/tex]
At earth, [tex]g=9.8\ m/s^2[/tex]
[tex]g'=1.63\ m/s^2[/tex]
As the value of g is less on the moon, so the time period on the moon increases.
(c) The time period on the earth, T = 3 s
On earth, [tex]T=2\pi\sqrt{\dfrac{l}{g}}[/tex]
[tex]3=2\pi\sqrt{\dfrac{l}{9.8}}[/tex]..............(1)
On moon, [tex]T'=2\pi\sqrt{\dfrac{l}{g'}}[/tex]
[tex]T'=2\pi\sqrt{\dfrac{l}{1.63}}[/tex]..............(2)
On solving equation (1) and (2),
T' = 18.03 s
Hence, this is the required solution.
