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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^(3)b^(2))/(dsqrt(c))`
The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2% respectively. What is the percentage errors in the quantity P?

Text Solution

Verified by Experts

Relative error in P is given by
`(DeltaP)/(P) = 3 (Deltaa)/(a) +2 (Deltab)/(b) + 1/2 (Deltac)/(c) + (Deltad)/(d)`
`(DeltaP)/(P) xx 100 = 3((Deltaa)/(a) xx 100) +2 ((Deltab)/(b) xx 100) +1/2 ((Deltac)/(c) xx 100)+ (Deltad)/(d) xx 100`
= `(3xx1%) + (2xx3%)+((1)/(2)xx4%)+(1xx2%) =13%`
Rounded off value of P = 3.8
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