Physics And Measurement Question 175
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 the maximum error in the value of a determined by the experiment is
Options:
A) ( $ b _{1}+c _{1}+d _{1}+e _{1} $ )%
B) ( $ {b _{1}}+c _{1}-d _{1}-e _{1} $ )%
C) ( $ \alpha b _{1}+\beta c _{1}-\gamma d _{1}-\delta e _{1} $ )%
D) ( $ \alpha b _{1}+\beta c _{1}+\gamma d _{1}+\delta e _{1} $ )%
Show Answer
Answer:
Correct Answer: D
Solution:
$ a={{b}^{\alpha }}{{c}^{\beta }}/{{d}^{\gamma }}{{e}^{\delta }} $
So maximum error in a is given by $ {{( \frac{\Delta 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} )% $
