Question

A physical parameter a can be determined by measuring the parameters b, c, d and e using the relation $a=\frac{b^{\alpha }{c}^{\beta }}{d^{\gamma }{e}^{\delta }}$. 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.

• A.
• B.
• C.
• D. none of these

Answer 1

The correct option is A

$a=\frac{b^{\alpha }{c}^{\beta }}{d^{\gamma }{e}^{\delta }}$

So maximum error in a is given by

${(\frac{△a}{a}\times 100)}_{max}=\alpha .\frac{\Delta b}{b}\times 100+\beta .\frac{\Delta c}{c}\times 100+\gamma .\frac{\Delta d}{d}\times 100+\delta \frac{\Delta e}{e}\times 100$ = $(\alpha b_1+\beta c_1+\gamma d_1+\delta e_1)\%$