A physical quantity A is related to four obse | vedclass

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Question

$A =\frac{ a ^{2} b ^{3}}{ c \sqrt{ d }}$

$\frac{\Delta a }{ a } 	imes 100=1 \%,$$ \frac{\Delta b }{ b } 	imes 100=3 \%,$$ \frac{\Delta c }{ c }

Vedclass · Accepted Answer

$14$

Vedclass · Answer

$A =\frac{ a ^{2} b ^{3}}{ c \sqrt{ d }}$

$\frac{\Delta a }{ a } 	imes 100=1 \%,$$ \frac{\Delta b }{ b } 	imes 100=3 \%,$$ \frac{\Delta c }{ c } 	imes 100=2 \%$ and $\frac{\Delta d }{ d } 	imes 100=2 \%$

$\frac{\Delta A }{ A } 	imes 100=2 \frac{\Delta a }{ a } 	imes 100+3 \frac{\Delta b }{ b } 	imes 100+$$\frac{\Delta c }{ c } 	imes 100+\frac{1}{2} 	imes \frac{\Delta d }{ d } 	imes 100$

$\frac{\Delta A }{ A } 	imes 100=2 	imes 1+3 	imes 3+2+\frac{1}{2} 	imes 2=14 \%$

A physical quantity $A$ is related to four observable $a,b,c$ 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 $A$ ......... $\%$

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