What is the change in the time period of simple pendulum if its length

1.	What is the change in the time period of simple pendulum if its length changes by 1%?
Answer» SOLUTION :Expression for the time period of a SIMPLE pendulum is `T= 2pisqrt((L)/(G))` ………..(1) Differentiating w.r.t l `(dT)/(DL)= ((2pi)/(sqrt(g))(1)/(2l^(1//2)))` `dT=((2pi)/(sqrt(g)))(1)/(2)(dl)/(2l^(1//2))` ……….(2) Dividing (2) with (1) `(dT)/(T)=(((2pi)/(sqrt(g)))(1)/(2)(dl)/(2l^(1//2)))/(((2pi)/(sqrt(g)))l^(1//2))` `((dT)/(T))%= (1)/(2)((dl)/(l))%` In this problem, % change in l =1% `:.` % change in `T= (1)/(2)(1)= 0.5%`

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