Question

Derive the relation between the time period of a simple pendulum and the factors on which it depends on.

Answer 1

We know T $\propto \sqrt{l}$
and T $\propto \frac{l}{\sqrt{g}}$
$\therefore T\propto \sqrt{\frac{l}{g}}$
T = k . $\sqrt{\frac{l}{g}}$ Where k is the constant of proportionality
It has been found experimentally that the value of the constant k is $2\pi$
$\therefore T=2\pi \sqrt{\frac{l}{g}}$