In a sample pendulum experiment, length is measured as `31.4cm` with an accuracy of `1mm`. The time for `100` ocscillations of pendulum is `112s` with an accuracy of `0.01s`. The percentage accuracy in `g` is

Explanation

(Accuracy is to be taken as the crror involved)
l= 31.4 cm and `Deltal = 1 mm = 0.1 cm`
`T=(112.0)/(100) = 1.12s` and `DeltaT = 0.01 s`
Formula for g is `g=4pi^(2)((l)/(T^(2)))`
`(Deltag)/(g)=((Deltal)/(l))+2((DeltaT)/(T))`
`=((0.1)/(31.4))+2((0.01)/(1.12))=0.003+0.02=0.023`
Relative error in determining g is 0.023 and `"percentage error" = 0.023 xx 100 = 2.3%`