Answer:
T' = 2T
Step-by-step explanation:
The time period of a simple pendulum is given by the relation as follows :
![T=2\pi \sqrt{(l)/(g)}](https://img.qammunity.org/2021/formulas/physics/college/h96qbyfu133gqyidc8e5lx2jif62xv72il.png)
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 :
![T'=2\pi \sqrt{(l')/(g)}\\\\T'=2\pi \sqrt{(4l)/(g)}\\\\T'=2* 2\pi \sqrt{(l)/(g)}\\\\T'=2* T](https://img.qammunity.org/2021/formulas/physics/college/ae1umuiqedrns496uq66ie71may86r0h0e.png)
So, the new time period is 2 times of the initial time period.