A physical quantity $A$ is related to four observables $a,\ b,\ c\ and\ d$ as follows $\ A = \frac{a^{2}b^{3}}{c\sqrt{d}}$ The percentage errors of measurement in $a,\ b,c\ and\ d$ are 1%, 3%, 2% and 2% respectively. What is the percentage error in the quantity $A?$

Question

Dr. Abubacker · Accepted Answer

Percentage error in $\ A = \left( 2\frac{\mathrm{\Delta}a}{a} + 3\frac{\mathrm{\Delta}b}{b} + \frac{\mathrm{\Delta}c}{c} + \frac{1}{2}\frac{\mathrm{\Delta}d}{d} ight) 	imes 100\%$ $\ = 2 	imes 1 + 3 	imes 3 + 2 + \frac{1}{2} 	imes 2$ $= 2 + 9 + 2 + 1 = 14\%$

Q. A physical quantity $A$ is related to four observables $a,\ b,\ c\ and\ d$ as follows $\ A = \frac{a^{2}b^{3}}{c\sqrt{d}}$ The percentage errors of measurement in $a,\ b,c\ and\ d$ are 1%, 3%, 2% and 2% respectively. What is the percentage error in the quantity $A?$

Explanation

Reviewed by Dr. Abubacker

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