'Ihe length of a pendulum is measured as 20.0 cm. The time interval for 100 oscillations is mea

step 1 The length of the pendulum is measured as 20 cm. The time interval for 100 oscillations is measu

'Ihe length of a pendulum is measured as 20.0 cm. The time...

'Ihe length of a pendulum is measured as $20.0 \mathrm{~cm}$. The time interval for 100 oscillations is measured as $90 \mathrm{~s}$ with a stop watch of $1 \mathrm{~s}$ resolution. The accuracy in the determination of $\mathrm{g}$ is
(a) $1 \%$
(b) $2 \%$
(c) $3 \%$
(d) $4 \%$

Key Concepts

Error Propagation

Error propagation involves determining how uncertainties in the measurement of individual quantities affect the uncertainty in a derived quantity. When a result is calculated from several measured values (such as using a formula involving length and time), the uncertainties of these measured values must be appropriately combined to estimate the overall uncertainty of the result.

Uncertainty Analysis in Pendulum Experiments

In simple pendulum experiments, the period is related to the length of the pendulum and the acceleration due to gravity by a mathematical formula. Analyzing the uncertainties in both the measured length and the measured time contributes to the final uncertainty in determining g, illustrating how experimental errors influence derived physical constants.

Instrument Resolution

Instrument resolution is the smallest increment that can be measured with an instrument, directly impacting the accuracy of measurements. The resolution sets a lower limit on how precise a measurement can be, and this limitation must be considered in uncertainty analysis since it often represents the dominant source of error.

Percentage Uncertainty

Percentage uncertainty offers a way to express the size of the error relative to the measured value. By converting an absolute uncertainty into a percentage, one can easily compare the precision of different measurements and understand the relative impact of measurement errors on the final result.

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