The period of oscillation of a simple pendulum is T = 2 π L / g . Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist

Question

The period of oscillation of a simple pendulum is T = 2 π L / g . Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1 s resolution. What is the accuracy in the determination of g (in percent)?

TestHub · Accepted Answer

g = 4 π 2 L T 2 T = t n Δ T = Δ t n Δ T T = Δ t t Δ g g = Δ L L + 2 Δ t t = 0.1 20.0 + 2 ( 1 90 ) = 0.005 + 0.0222 = 0.027 Thus the percentage error in g is 2.7%.

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