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A physical quantity 'x' is given by the ...

A physical quantity 'x' is given by the relation
`x=(a^(2)b)/(sqrt(c ))`
If errors in a, b and c are `2%` and `3%` and `4%` respectively, calculate percentage error in 'x'.

Text Solution

Verified by Experts

We are given
`(Delta)/(a)=2%`, `(Deltab)/(b)=3%` and `(Deltac )/(c )=4%`
We know that percentage error in x is
`(Deltax)/(x)=2(Deltaa)/(a)+(Deltab)/(b)+(1)/(2)(Deltac)/(c )=2xx2%+3%+(1)/(2)xx4%`
`=4%+3%+2%=9%`
So percentage error in x is `9%`.
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