Physics

Problem

(i) Define fractional (relative) uncertainty of a physical quantity. (ii) A student measures two lengths required to calculate the area of a narrow strip. She records length

x = 15.2\,\text{cm}

with an absolute uncertainty of

\pm 0.1\,\text{cm}

, and breadth

y = 0.36\,\text{cm}

with an absolute uncertainty of

\pm 0.01\,\text{cm}

. Calculate the fractional uncertainty for each measurement. (iii) Using your results of part (ii), explain quantitatively why quoting only absolute uncertainties would give a misleading impression of the precision of the two measurements when they are later multiplied to obtain the area. Support your explanation with suitable numerical comparison.

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