In an experiment to determine the value of acceleration due to gravity g using a simple pendulum , the measured value of lenth of the pendulum is 31.4 cm known to 1 mm accuracy and the time period for 100 oscillations of pendulum is 112.0 s known to 0.01 s accuracy . find the accuracy in determining the value of g.

Explanation

(Accuracy is to be taken as the error involved )
`1=31.4"and"Delta1=1mm=0.1cm`
`T=(112.0)/(100)=1.12s"and "Delta1=1mm=0.1cm`
Formula for g is `g=4pi^(2)(l/T^(2))`
`(Deltag)/g=((Deltal)/l)+2((DeltaT)/T)`
`=((0.1)/(31.4))+2((0.001)/(1.12))`
`=0.003+0.02=0.023`
Relative error in determining g is `0.023`and percentage error`=0.023xx100=2.3%`