Question

The time periods of two pendulums are 1.44 s and 0.36 s respectively. Calculate the ratio of their lengths.

Answer 1

`"T"_1` = 1.44 s;
`"T"_2` = 0.36 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)=1.44/0.36=144/36=4/1`

Squaring both sides,

`(sqrt(("l"_1)/"l"_2))^2=(4/1)^2`

⇒ `"l"_1/"l"_2=16/1`