The least count of a stop watch is 1 / 5 s. The time of 20 oscillations of a pendulum is measur

step 1 Hi everyone here it is given least count of stopwatch is 1 by 5 second time measured is 25 secon

The least count of a stop watch is 1 / 5 s. The time of 20...

The least count of a stop watch is $1 / 5 \mathrm{~s}$. The time of 20 oscillations of a pendulum is measured to be $25 \mathrm{~s}$. The minimum percentage error in the measurement of time will be
(A) $0.1 \%$
(B) $0.8 \%$
(C) $1.8 \%$
(D) $8 \%$

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Key Concepts

Least Count

Least count is the smallest value that can be measured by an instrument. It determines the instrument’s resolution and directly influences the precision of any measurement taken with that instrument. In error analysis, the least count represents the smallest uncertainty in reading, affecting the overall accuracy of the measurement.

Absolute Error

Absolute error refers to the magnitude of the uncertainty inherent in a measurement, typically equal to the instrument’s least count or half of it, depending on the instrument and procedure. It quantifies the maximum expected deviation of the measured value from the true value, forming the basis of error analysis.

Relative Error and Percentage Error

Relative error is the ratio of the absolute error to the measured value, providing a scale-independent measure of precision. When this ratio is multiplied by 100, it is expressed as percentage error, which offers a clear quantitative assessment of the measurement’s accuracy relative to its magnitude. This is especially important when comparing uncertainties across different measurements.

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