The side of a square plate is measured once as

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Uncertainty in measurement

Mathematical Methods for Physics, Ch Probability, random variables and distributions

Problem

L = 50.0 \pm 0.2\,\mathrm{mm}

, and the area is computed as

A = L\times L

. A student treats the two factors as independent and adds their relative uncertainties in quadrature, obtaining a relative uncertainty in

A

0.57

per cent. ((a)) Find the error in this reasoning, and give the area with its correct uncertainty. ((b)) A second plate is rectangular. Its two sides are measured separately, each reading with its own independent error, as

a = 50.0 \pm 0.2\,\mathrm{mm}

and

b = 30.0 \pm 0.2\,\mathrm{mm}

. Say which way of combining the two contributions applies now, and give the area with its uncertainty.

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