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