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A physical quantity z depends on four observables a,b,c and d as z=\frac{a^{2}b^{\frac{2}{3}}}{\sqrt{c}\; d^{3}}. THe percentages of error in the measurment of a,b,c and d are 2\; ^{o}/_{o},1.5\; ^{o}/_{o},4\; ^{o}/_{o} and 2.5\; ^{o}/_{o} respectively. The percentage of error in z is :
Option: 1 12.25\; ^{o}/_{o}  
Option: 2 16.5\; ^{o}/_{o}
Option: 3 13.5\; ^{o}/_{o}
Option: 4 14.5\; ^{o}/_{o}

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\frac{\Delta Z}{Z}=\frac{2 \Delta \mathrm{a}}{\mathrm{a}}+\frac{2}{3} \frac{\Delta \mathrm{b}}{\mathrm{b}}+\frac{1}{2} \frac{\Delta \mathrm{c}}{\mathrm{c}}+\frac{3 \Delta \mathrm{d}}{\mathrm{d}}=14.5 \%

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Deependra Verma

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