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A physical quantity X is related to four...

A physical quantity X is related to four measurable quantities a, b, c and d as follows `X=a^(2)b^(3)c^((5)/(2))d^(-2)`. The percentange error in the measurement of a, b, c and d are 1 %, 2%, 3% and 4% respectively. What is the percentage error in quantity X? If the value of X calculated on the basis of the above relation is 2.763. to what value should you round off the result.

Text Solution

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Given physical quantity `X=a^(2)b^(2)c^((5)/(2))d^(-2)`
Maximum percentage error in x s,
`(DeltaX)/(X)xx100=[2((Deltaa)/(a)xx100)+3((Deltab)/(b)xx100)+(5)/(2)((DeltaC)/(c)x100)+2((Deltad)/(d)xx100)]`
`=[(2(1)+3(2)+(5)/(2)(3)+2(4)]%`
`=[2+6+(15)/(2)+8]=+-23.5%`
`:.` Percentage error in `X=23.5%`
Relative error in X = 0.235 = 0.24
(By rounding off upto two significant figures) The calculated value of x should be round off upto two significant digits
`:. 2.8`
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