Answer:
The length of the simple pendulum is 2.4 meters.
Explanation:
Time period of simple pendulum is given by :
[tex]T=2\pi\sqrt{\dfrac{L}{g}}[/tex]
L is the length of pendulum
The time period of the rope is given by :
[tex]T=2\pi\sqrt{\dfrac{2L'}{3g}}[/tex]
L' is the length of the rod, L' = 3.6 m
It is given that, the rod have the same period as a simple pendulum and we need to find the length of simple pendulum i.e.
[tex]2\pi\sqrt{\dfrac{L}{g}}=2\pi\sqrt{\dfrac{2L'}{3g}}[/tex]
On solving the above equation as :
[tex]\dfrac{L}{g}=\dfrac{2L'}{3g}[/tex]
L = 2.4 m
So, the length of the thin rod that is hung vertically from one end and set into small amplitude oscillation 2.4 meters. Hence, this is the required solution.
