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A physcial quantity X is related to fou...

A physcial quantity X is related to four measurable quantites a, b, c and d as follows : `X = a^2 b^3 c^(5//2) d^(-2)` The percentage 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 is `X=a^(2)b^(3)c^(5//2)d^(-2)`
Maximum percentage error in X is
`(DeltaX)/Xxx100=+-[2((Deltaa)/axx100)+3((Deltab)/bxx100)+5/2((Deltac)/cxx100)+2((Deltad)/d xx100)]`
`=+-[2(1)+3(2)+5/2(3)+2(4)]%`
`=+-[2+6+15/2+8]=+-23.5%`
`therefore" Percentage error in quantity "X=+-23.5%`
Mean absolute error in `X=+-0.235=+-0.24` (rounding -off upto significant digits)
The calculated value of x should be round-off upto two significant digits.
`therefore X=2.8`
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