Answer:
T' = 2T
Explanation:
The time period of a simple pendulum is given by the relation as follows :
[tex]T=2\pi \sqrt{\dfrac{l}{g}}[/tex]
l is length of the pendulum
g is acceleration due to gravity
If the length is increased four time, new length is l' = 4l
So,
New time period is :
[tex]T'=2\pi \sqrt{\dfrac{l'}{g}}\\\\T'=2\pi \sqrt{\dfrac{4l}{g}}\\\\T'=2\times 2\pi \sqrt{\dfrac{l}{g}}\\\\T'=2\times T[/tex]
So, the new time period is 2 times of the initial time period.
