A simple pendulum consisting of a mass M attached to a string of length L is released from rest at an angle $\alpha$. A pin is located at a distance$\ell$ below the pivot point. When the pendulum swings down, the string hits the pin as shown in the figure. The maximum angle $\theta$ which string makes with the vertical after hitting the pin is


            

Given below are two statements:
Statement $\mathrm{I}$: A second's pendulum has a time period of $1$ second.

Statement $\mathrm{II}$: It takes precisely one second to move between the two extreme positions. In the light of the above statements,

choose the correct answer from the options given below

A simple pendulum has time period $T_1$. The point of suspension is now moved upward according to the relation $y=k{t}^2,\left(k=1 \mathrm{m} {\mathrm{s}}^{-2}\right)$  where $y$ is the vertical displacement. The time
period now becomes $T_2$.

The ratio of $\frac{T_1^2}{T_2^2}\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$ is