A physical quantity `x` is calculated from the relation `x = ( a^(2) b^(3))/(c sqrt( d))`. If the percentage error in `a, b , c , and d are 2% , 1% , 3%, and 4%`, respectively , what is the percentage error in `x`?

Options

A. `""pm8%`
B. `""pm10%`
C. `""pm14%`
D. `""pm12%`

Answer

C

Explanation

`Q=(A^(3)B^(3))/(Csqrt(D))`
`(DeltaQ)/(Q)=3((DeltaA)/(A))+3((DeltaB)/(B))+((DeltaC)/(C))+(1)/(2)((DeltaD)/(D))`
Given that, `(DeltaA)/(A)xx100=2,(DeltaB)/(B)xx100=1`
`(DeltaC)/(C)xx100=3,(DeltaD)/(D)xx100=4`
`therefore" "(DeltaQ)/(Q)xx100=(3xx2)+(3xx1)+(3)+(1)/(2)xx(4)`
`=pm14%`