Answer:
[tex]T^2 \propto L[/tex]
Explanation:
The period of a simple pendulum is given by:
[tex]T=2\pi \sqrt{\frac{L}{g}}[/tex]
where
L is the length of the pendulum
g is the acceleration of gravity
From this equation we can write
[tex]T\propto \sqrt{L}\\T\propto \frac{1}{\sqrt{g}}[/tex]
Taking the square of this equation, we get:
[tex]T^2 = (2\pi)^2 \frac{L}{g}[/tex]
So we see that [tex]T^2[/tex] is proportional to L and inversely proportional to g. So, we can write:
[tex]T^2 \propto L\\T^2 \propto \frac{1}{g}[/tex]
So the only correct option is
[tex]T^2 \propto L[/tex]
