A physical parameter a can be determined by measuring the paramet… - Vidyadip

MCQ

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
$\left(\alpha b_1+\beta c_1-\gamma d_1-\delta e_1\right) \%$
✓
$\left(\alpha b_1+\beta c_1+\gamma d_1+\delta e_1\right) \%$

✓

Answer

Correct option: D.

$\left(\alpha b_1+\beta c_1+\gamma d_1+\delta e_1\right) \%$

(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 $ $+\gamma \cdot \frac{\Delta d}{d} \times 100+\delta \cdot \frac{\Delta e}{e} \times 100$
$=\left(\alpha b_1+\beta c_1\gamma d_1+\delta e_1\right) \%$

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