A Physical quantity P is related to four observables a,b,c and d as follows:
`P=(a^3b^2)/(sqrtc d)`
The percentage errors of measurement in a,b,c and d are `1%`,`3%`,`4%` and `2%` respectively. What is the percentage error in the quantity P? If the value of P calculated using the above relation turns out to be `3.763`, to what value should you round off the result?

Options

A. `10%`
B. `13%`
C. `5%`
D. `15%`

Answer

B

Explanation

Given, `P=(a^(3)b^(2))/(sqrt(c)d)=a^(3)b^(2)c^(-1//2)d^(-1)`
The fractional error in P is given by
`" "(DeltaP)P=3""(Deltaa)/a+2""(Deltab)/b-1/2*(Deltac)/c-(Deltad)/d`
The maximum fractional error in P is
`" "((DeltaP)/P)=3(Deltaa)/a+2(Deltab)/b+1/2(Deltac)/c+(Deltad)/d`
The percentage error in P is
`" "((DeltaP)/P)_("max") times 100=3((Deltaa)/a times 100) +2((Deltab)/b times 100)+1/2((Deltac)/c times 100)+((Deltad)/d times 100)`
= 3 (% error in a) + 2 (% error in b) + `1/2` (error in c) + (% error in d)
`=3(1%)+2(3%)+1/2(4%)+(2%)`
`=3%+6%+2%+2%=13%`