Question

When length of simple pendulum is increased by 22 cm, the period change by 20,% find
the original length of simple pendulum.​

Answer 1

Given that,

Increased length = 22 cm

Changing percentage of time period = 20 %

Let the original length is l and time period is T.

The changing length is

$l'=l+0.22$

The changing time period is

$T'=(1+0.2)T$

$T'=1.2 T$

We know that,

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

$T\propto\sqrt{l}$

We need to calculate the original length of simple pendulum

Using formula of time period

$\dfrac{T}{T'}=\dfrac{\sqrt{L}}{\sqrt{L'}}$

$\dfrac{T^2}{T'^2}=\dfrac{l}{l'}$

Where, T = time period

T' = changing time period

l = original length

l' = changing length

Put the value into the formula

$\dfrac{T^2}{(1.2 T)^2}=\dfrac{l}{l+0.22}$

$\dfrac{1}{1.44}=\dfrac{l}{l+0.22}$

$l+0.22=1.44l$

$l=\dfrac{0.22}{0.44}$

$l =0.5\ m$

$l=50\ cm$

Hence. The original length of simple pendulum is 50 cm.