In an experiment to determine the acceleration due to gravity ( g ) using a simple pendulum, the length of the pendulum is measured as 100.0 cm using a meter scale of least count 1 mm . The time for 20 oscillations is measured as 40.0 s using a stopwatch of least count 0.1 s . The maximum percentage error in the determination of g is :

Step-by-step solution

The formula for the acceleration due to gravity is g = 4 ^2 L T^2 Since the time for n oscillations is t = nT , we have T = t n . Thus, the relative error in T is the same as the relative error in t : T T = t t . The expression for the maximum percentage error in g is: ( g g 100 ) = ( L L 100 ) + 2 ( t t 100 ) From the given data: L = 100.0 cm , L = 1 mm = 0.1 cm t = 40.0 s , t = 0.1 s Calculating the individual percentage errors: Percentage error in L = 0.1 100.0 100 = 0.1 % Percentage error in t = 0.1 40.0 100 =