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A physical quantity P is related to four...

A physical quantity P is related to four observables a, b, c and d as follows :- `P=a^3b^2//((sqrtc)d)` The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%, respectively. What is the percentage error in the quantity P? If the value of Pcalculated using the above relation turns out to be 3.763, to what value should you round off the result ?

Text Solution

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We are given : `(Deltaa)/(a)=1%`, `(Deltab)/(b)=3%`, `(Deltac)/(c )=4%`, `(Deltad)/(d)=2%`
Percentage error in P is `(DeltaP)/(P)=3(Deltaa)/(a)+2(Deltab)/(b)+(1)/(2)(Deltac)/(c )+(Deltad)/(d)`
`=3xx1%+2xx3%+(1)/(2)xx4%+2%=3%+6%+2%+2%`
`:.(DeltaP)/(P)=13%`
The result has two significant figures, so if P turns out of be `3.763`, the result would be rounded off to `3.8`.
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