In an experiment to determine the acceleration due to gravity ( g ) using a simple pendulum, a student measures the length of the pendulum as (100.0 0.1) cm and the time period as (2.00 0.02) s . The maximum percentage error in the measurement of g will be:

Step-by-step solution

The acceleration due to gravity g determined by a simple pendulum is given by g = 4 ^2 L T^2 . The maximum percentage error in g is given by the sum of the fractional errors of the individual quantities, taking into account their powers: g g 100 = L L 100 + 2 ( T T 100 ) Given L = (100.0 0.1) cm and T = (2.00 0.02) s , we calculate the individual percentage errors: Percentage error in L = ( 0.1 100.0 ) 100 = 0.1 % Percentage error in T = ( 0.02 2.00 ) 100 = 1.0 % Substituting these into the error equation: Maximum