A physical quantity P is related to four observables a, b, c and d as follows: `P= (a^(3)b^(2))/(sqrt(c)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?

Options

A. `12%`
B. `13%`
C. `15%`
D. `16%`

Answer

B

Explanation

As `P= (a^(3)b^(2))/(sqrt(c)d)`
The percentage error in P is
`(DeltaP)/(P)xx100= [3((Deltaa)/(a))+ 2((Deltab)/(b))+ (1)/(2)((Deltac)/(c))+ (Deltad)/(d)] xx 100`
`[ 3 xx 1%+ 2 xx 3%+ (1)/(2) xx 4%+ 2%]= 13%`