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 cm and Delta 1 = 1 ` mm =0.1 cm
`T = (112.0)/(100) = 1.12s and Delta T = 0.01s`
Formula for g is g `= 4pi^2 ((l)/(T^2))`
`(Deltag)/g =((Deltal)/(l)) + 2((DeltaT)/(T))`
`=((0.1)/(31.4)) + 2 ((0.1)/(1.12))`
`=0.003 + 0.02 = 0.023`
Relative error in determining g is 0.023 and percentage error `=0.023xx100 = 2.3 %`