Question

The time period of the two pendulums are 2 s and 3 s respectively. Find the ratio of their lengths.

Answer 1

`"T"_1` = 2 s;
`"T"_2` = 3 s
Let l₁ and l₂ be the lengths of the two pendulums.

`"T"_1/"T"_2=sqrt("l"_1/"l"_2)`

`sqrt("l"_1/"l"_2)=2/3`

Squaring both sides,

`(sqrt(("l"_1)/"l"_2))^2=(2/3)^2=4/9`

`sqrt("l"_1/"l"_2)=4/9` = 4 : 9