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An experiment measures quantities a,b,c ...

An experiment measures quantities a,b,c and d and x is calculated from formula
`x=(ab^(1//2))/(c^(3//2)d^(3))`.
The percentage errors in a,b,c and d are `2%`, `4%` `, 6%` and `1%` respectively. What is the percentage error in x ?

Text Solution

Verified by Experts

We are given : `(Deltaa)/(a)=2%`, `(Deltab)/(b)=4%`, `(Deltac)/(c )=6%` and `(Deltad)/(d)=1%`
We know that , percentage error in x is
`(Deltax)/(x)=(Deltaa)/(a)+(1)/(2)(Deltab)/(b)+(3)/(2)(Deltac)/(c )+3(Deltad)/(d)`
`=2%+(1)/(2)xx4%+(3)/(2)xx6%+3xx1%=2%+2%+9%+3%=16%`
`:.(Deltax)/(x)=16%`
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