For a simple pendulum, the time period is given by T = 2π√(L/g). The length L is measured as 20.0 cm with an uncertainty of 1 mm, and the time taken for 100 oscillations is recorded as 90 s using a wristwatch having 1 s resolution. What is the percentage uncertainty in the calculated value

Question

For a simple pendulum, the time period is given by T = 2π√(L/g). The length L is measured as 20.0 cm with an uncertainty of 1 mm, and the time taken for 100 oscillations is recorded as 90 s using a wristwatch having 1 s resolution. What is the percentage uncertainty in the calculated value of g?

Accepted Answer

3%. g = 4*pi^2*L/T^2, so dg/g = dL/L + 2*dT/T. dL/L = 0.1/20.0 = 0.5%. For 100 oscillations in 90 s with 1 s resolution, dT/T = 1/90, so 2*dT/T = 2.22%. Total = 0.5% + 2.22% = 2.7% -> approximately 3%.

For a simple pendulum, the time period is given by T = 2π√(L/g). The length L is measured as 20.0 cm with an uncertainty of 1 mm, and the time taken for 100 oscillations is recorded as 90 s using a wristwatch having 1 s resolution. What is the percentage uncertainty in the calculated value of g?

Solution

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