Question

A physical parameter $a$ can be determined by measuring the parameters $b,c,d$ and $e$ using the relation $a=b^{\alpha }{c}^{\beta }/d^{\gamma }{e}^{\delta }$. If the maximum errors in the measurement of $b,c,d$ and $e$ are $b_1\%,c_1\%,d_1\%$ and $e^1\%$, then the maximum error in the value of $a$ determined by the experiment is

• A. $\left(b_1+c_1+d_1+e_1\right)\%$
• B. $\left(b_1+c_1-d_1-e_1\right)\%$
• C. $\left(\alpha b_1+\beta c_1-\gamma d_1-\delta e_1\right)\%$
• D. $\left(a{b}_1+\beta c_1+\gamma d_1+\delta e_1\right)\%$

Answer 1

Answer: (D)

$a=b^{\alpha }{c}^{\beta }/d^{\gamma }{e}^{\delta }$
So, maximum error in $a$ is given by
${\left(\frac{\Delta a}{a}\times 100\right)}_{\max }=\alpha \cdot \frac{\Delta b}{b}\times 100+\beta \cdot \frac{\Delta c}{c}\times 100$
$+\gamma \cdot \frac{\Delta d}{d}\times 100+\delta \cdot \frac{\Delta e}{e}\times 100$
$=\left(\alpha b_1+\beta c_1+\gamma d_1+\delta e_1\right)\%$