Question

The time periods of two simple pendulums at a place are in ratio 2 : 1. What will be the corresponding ratio of their lengths ?

Answer 1

$T_1:T_2::2:1$

$2\pi \sqrt{\frac{l_1}{g}}:2\pi \sqrt{\frac{l_2}{g}}::2:1$

$\sqrt{l_1}:\sqrt{l_2}::2:1$

square both sides

$(\frac{\sqrt{l_1}}{\sqrt{l_2}}{)}^2=(\frac{2}{1}{)}^2$

$l_1:l_2::4:1$