The period of oscillation of a simple pendulum is given by T = 2 l g where l is about 80 cm and is known to have 0.1 cm accuracy. The period is about 1.5 s. The time of 50 oscillations is measured by a stop watch of least count 0.1 s. The percentage error in g is nearly

Step-by-step solution

The formula for the time period of a simple pendulum is T = 2 l g . Rearranging for g , we get: g = 4 ^2 l T^2 The percentage error in g is given by: g g 100 = ( l l + 2 T T ) 100 Given values are: l = 80 cm, l = 0.1 cm The time for 50 oscillations is t = 50 1.5 = 75 s. The error in measuring the total time is the least count of the stopwatch, so t = 0.1 s. Since T = t 50 , the relative error in T is the same as the relative error in t : T T = t t = 0.1 75 Substituting these values into the error equation: g g 100