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Question

If there is an error of 2% in measuring the length of a simple pendulum, then percentage error in its period is
(a)1%
(b) 2%
(c) 3%
(d) 4%

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Solution

(a) 1%
Let l be the length if the pendulum and T be the period.

Also, let l be the error in the length and T be the error in the period.We havell×100=2dll×100=2Now, T=2πlgTaking log on both sides, we getlog T=log 2π+12log l-12log gDifferentiating both sides w.r.t. x, we get1TdTdl=12ldTdl=T2ldll×100=2dTT×100dTT×100=22TT×100=1Hence, there is an error of 1% in calculating the period of the pendulum.

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