Question 167: Units , Dimensions and Error Analysis

Question

A physical quantity z depends on four
observables a, b, c and d, as z = $${{{a^2}{b^{{2 \over 3}}}} \over {\sqrt c {d^3}}}$$. The
percentages of error in the measurement of a,
b, c and d are 2%, 1.5%, 4% and 2.5%
respectively. The percentage of error in z is :

Accepted Answer

z = $${{{a^2}{b^{{2 \over 3}}}} \over {\sqrt c {d^3}}}$$
$$ \Rightarrow $$ $${{dz} \over z} 	imes 100 = \left( {2{{da} \over a} + {2 \over 3}{{db} \over b} + {1 \over 2}{{dc} \over c} + 3{{d\left( d ight)} \over d}} ight) 	imes 100$$
% error in z
= $$\left( {2 	imes 2 + {2 \over 3} 	imes 1.5 + {1 \over 2} 	imes 4 + 3 	imes 2.5} ight) $$ %
= ( 4 + 1 + 2 + 7.5 ) %
= 14.5 %

Answer

13.5 %

Answer

14.5%

Answer

16.5%

Answer

12.25%

Units , Dimensions and Error Analysis

A physical quantity z depends on four observables a, b, c and d, as z = ${{{a^2}{b^{{2 \over 3}}}} \over {\sqrt c {d^3}}}$. The percentages of error in the measurement of a, b, c and d are 2%, 1.5%, 4% and 2.5% respectively. The percentage of error in z is :

Choose the correct answer: