Question

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A determining the specific gravity by the formula S = where A - w A is the weight in air, w is the weight in water, A can be read within 0.01 gm and w within 0.02 gm. Find approximately the maximum error in S if the readings are A 1.1 gm, w = 0.6 gm. Find also the maximum relative error

Answer 1

S = A/A - W Differentiating above equation delta S = (A - w) delta A - A delta (A - w)/(A - w)^2 delta s = (A - w) delta A - A [delta A - delta w]/(Aw)^2 maximum error in s can be obtained if we take delta A = -0.01 and delta w = 0.02 delta s = (1.1 - 0.6) [- 0.01] - (1.1) [- 0.01 - 0.02]/(1.1 - 0.6)^2 delta s = (0.5) (- 0.01) - (1.1) (- 0.03)/(0.5)^2 delta s = -5 times 10^- 3 - (- 33 times 10^- 3)/0.25 = -5 times 10^- 3 + 33 times 10^- 3/250 times 10^- 3 delta s = 28 times 10^- 3/250 times 10^- 3 = 0.112 delta s = 0.112 maximum relative error in s = (delta s)_max/s = 0.112/(1.1/1.1 - 0.6) s = 0.05091