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Find the relative error in Z, if Z=A^(4)...

Find the relative error in Z, if `Z=A^(4)B^(1//3)//CD^(3//2)` and the percentage error in the measurements of A,B,C and D are 4%,2%,3% and 1% respectively.

Text Solution

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`(DeltaZ)/Z=4((DeltaA)/A)+1/3((DeltaB)/B)+(DeltaC)/C+3/2((DeltaD)/D)`
Given that, `(DeltaA)/Axx100=4(DeltaB)/Bxx100=2,(DeltaC)/Cxx100=3`
and `(DeltaD)/Dxx100=1`
`therefore(DeltaZ)/Zxx100=(4xx4)+(1/3xx2)+3+(3/2xx1)`
`=16+2/3+3+3/2=21.16%`
The percentage error in the measurement of Z is 21.16%.
Therefore, the relative error in Z is 0.2116
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