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  • A physical parameter a can be determined by measuring the parameters b, c, d and e using the relation <img alt="a=\frac{b^\alpha c^\beta}{d^\gamma e^\delta }" src="http://entrancecorner.o

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 the maximum error in the value of a determined by the experiment is

Option: 1

(b_1+c_1+d_1+e_1)\%


Option: 2

(b_1+c_1-d_1-e_1)\%


Option: 3

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


Option: 4

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


Answers (1)

best_answer

Given, \frac{\Delta b}{b}=b_1, \frac{\Delta c}{c}=c_1, \frac{\Delta d}{d}=d_1 &  \frac{\Delta e}{e}=e_1

The maximum error in a is given by:-

(\frac{\Delta a}{a}\times100)=(\alpha \frac{\Delta b}{b}\times100)+(\beta \frac{\Delta c}{c}\times100)+(\gamma \frac{\Delta d}{d}\times100)+(\delta \frac{\Delta e}{e}\times100)

=\alpha b_1+\beta c_1+\gamma d_1+\delta e_1

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chirag

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