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 0.1) cm and its time period of oscillation is measured as (2.00 0.02) s . The maximum percentage error in the calculated value of g will be

Step-by-step solution

The time period of a simple pendulum is given by T = 2 l g . Squaring both sides and rearranging for g , we get: g = 4 ^2 l T^2 The maximum relative error in g is given by: g g = l l + 2 T T Percentage error in length l is: l l 100 = 0.1 100.0 100 = 0.1 % Percentage error in time period T is: T T 100 = 0.02 2.00 100 = 1.0 % Therefore, the maximum percentage error in g is: ( g g 100 ) = 0.1 % + 2(1.0 %) = 2.1 % Answer: 2.1 %