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.

In an experiment to determine the value of acceleration due to gravity

1.	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.
Answer» Solution :(Accuracy is to be taken as the error involved) `l= 31.4 CM and Delta l= 1mm = 0.1cm` `T= (112.0)/(100) = 1.12s and Delta T = 0.01s` Formula for g is `g= 4PI^(2) ((l)/(T^(2)))` `(Delta g)/(g) = ((Delta l)/(l)) + 2 ((Delta T)/(T))` `=((0.1)/(31.4)) + 2 ((0.01)/(1.12)) = 0.003 + 0.02 = 0.023` RELATIVE error in determing g is 0.023 and PERCENTAGE error `= 0.023 xx 100= 2.3%`