In an experiment to determine the acceleration due to gravity ( g ) using a simple pendulum, the formula used is g = 4 ^2 L T^2 . If the maximum percentage error in the calculated value of g is 6 % and the percentage error in the measurement of length L is 2 % , then the percentage error in the measurement of time period T is

Step-by-step solution

The formula for the acceleration due to gravity is: g = 4 ^2 L T^2 The maximum percentage error in g is the sum of the percentage errors in the measured quantities, multiplied by the absolute values of their respective powers. Constants like 4 ^2 do not contribute to the error. g g 100 = ( L L 100 ) + 2 ( T T 100 ) Given: Maximum percentage error in g = 6 % Percentage error in L = 2 % Substituting the values: 6 % = 2 % + 2 ( T T 100 ) 2 ( T T 100 ) = 6 % - 2 % = 4 % T T 100 = 4 % 2 = 2 % The percentage error in the