A physical quantity `P=(a^(3)b^(2))/(sqrt(cd))` the percentage errors in measurement in a,b,c,d are 1%, 3%,4% and 2% respectively. What is the percentage error in measurement of quantity P?

Explanation

`P=(a^(3)b^(2))/(sqrtcd)`
Percentage error in P
`=(DeltaP)/(P)=(3(Deltaa)/(a)+2(Deltab)/(b)+(1Deltac)/(2)+(Deltad)/(d))xx100`
So, `(DeltaP)/(P)xx100 =3xx(Deltaa)/(a)xx100+2xx(Deltab)/(b)xx100 +(1)/(2)xx(Deltac)/(c)xx100 +(1)/(2)xx(Deltad)/(d)xx100`
`:.` Percentage error in P
=3 (% error in a) +2 (% error in d)
=`3xx 1% +2 xx3% +(1)/(2) xx4% +(1)/(2) xx2%`
`=3% +6%+2%+1% =12%`