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 find the maximum error in the value of a determined by the experiment.

Answer 1

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