Physics - SHM Question with Solution | TestHub

The time period of a simple pendulum is given by $T=2\pi \sqrt{\frac{l}{g}}$.

This implies $T\propto \sqrt{l}$, or $l\propto T^2$.

Given that the periodic time increases by $20\%$, the new time period is $T_2=T_1+0.20T_1=1.2T_1$.

The ratio of the lengths is:

$\frac{l_2}{l_1}={\left(\frac{T_2}{T_1}\right)}^2$

$\frac{l_2}{l_1}=(1.2{)}^2=1.44$

Answer: 1.44