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  • The physical parameter a can be determined by measuring the parameters b, c, d and e using the ra

The physical parameter a can be determined by measuring the parameters b, c, d and e using the ratio  a\ =\ \frac{b^\alpha c^\beta}{d^\gamma e^\delta}. If the measurement errors of b, c, d , and e are b_{1}%,\, c_{1}%, \, d_{1}%,\, and\, e_{1}%  maximum, then the maximum error of the experimentally measured values is:

Option: 1

\left(b_1+c_1+d_1+e_1\right)%


Option: 2

\left(b_1+c_1+d_1-e_1\right)%


Option: 3

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


Option: 4

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


Answers (1)

best_answer

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

So, maximum error is given by:

\left(\frac{\Delta a}{a} \times 100\right)_{\max }=\alpha \times \frac{\Delta b}{b} \times 100+\beta \times \frac{\Delta c}{c} \times 100+\gamma \times \frac{\Delta d}{d} \times 100+\delta \times \frac{\Delta e}{e} \times 100

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

 

Posted by

Rishi

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