The period of oscillation of a simple pendulum is T = 2 (L/g)^ 1/2 . Measured value of 'L' is 10 cm known to 1 mm accuracy and time for 100 oscillations is 50 second, using a watch of 1 second resolution. The percentage error in the measurement of 'g' is

Step-by-step solution

The formula for 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 percentage error in the measurement of g is: g g 100 = ( L L + 2 T T ) 100 Given the measured value of length L = 10 cm and accuracy L = 1 mm = 0.1 cm . The percentage error in length is: L L 100 = 0.1 10 100 = 1 % The time for 100 oscillations is t = 50 s and the resolution of the watch is t = 1 s . Since T = t n , the relative error in T is the same as the rel