Compare the time periods of two pendulums of length 1m and 9m.

As we know that,

$T = 2 π \sqrt{\dfrac{l}{g}} \\[0.5em]$

Time period is directly proportional to the square root of the length of the pendulum.

In the case when length is 1m,

$T_1 = 2 π \sqrt{\dfrac{1}{g}} \\[0.5em]$

and

In the case when length is 9m,

$T_2 = 2 π \sqrt{\dfrac{9}{g}} \\[0.5em]$

So, comparison of T₁ and T₂ gives —

$T$1 : T2 = 2 π \sqrt{\dfrac{1}{g}} : 2 π \sqrt{\dfrac{9}{g}} \\[0.5em] T1 : T2 = \sqrt{\dfrac{1}{9}} \\[0.5em] \Rightarrow T1 : T2 = \dfrac{1}{3} \\[0.5em]

Hence, T₁ : T₂ = 1 : 3