A physical quantity `Q` is calculated according to the expression
`Q=(A^(3)B^(3))/(CsqrtD)`
If percentage errors in `A, B, C, D` are 2%, 1%, 3% and 4% respectively. What is the percentage error in `Q`?

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%`