In the simple-pendulum experiment to measure g, a bob on a thread is hung from a fixed point. The thread length L (corrected for the bob/hook size) is measured, and the time for 50 oscillations gives the period T = (total time)/50. Repeating for several lengths and plotting L versus T² yie

Question

In the simple-pendulum experiment to measure g, a bob on a thread is hung from a fixed point. The thread length L (corrected for the bob/hook size) is measured, and the time for 50 oscillations gives the period T = (total time)/50. Repeating for several lengths and plotting L versus T² yields a straight line, with g = 4*pi² L/T². Which statement best describes the dominant errors in this experiment?

Accepted Answer

Both systematic and statistical errors are present; the systematic offset in L can be reduced by fitting the L vs T² points to a straight line.. Both error types occur: random (statistical) errors in reading length and timing, and systematic errors such as a constant uncertainty in the effective length and the finite-amplitude correction. Plotting L vs T² and fitting a line lets the slope give g while absorbing/identifying a constant systematic offset in L (the intercept), making this the most complete statement.

Solution

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