A physical quantity `P = (sqrt(abc^2) )/(d^3 e^(1//3) )` is determined by measuring a,b,c,d and e separately with the percentage error of 2%, 3% , 2%, 1% and 6% respectively. Minimum amount of error is contributed by the measurement of :

Options

A. b
B. a
C. d
D. c

Answer

B

Explanation

As `P= (sqrt(abc^(2)))/(d^(3))`
`:. (DeltaP)/(P) xx 100= [(1)/(2)(Deltaa)/(a)+ (1)/(2)(Deltab)/(b)+ (Deltac)/(c)+3(Deltad)/(d)] xx 100`
`= [(1)/(2) xx %+ (1)/(2) xx 3%+ 2^+3 xx 1]= [1%+ (3)/(2)%+ 2%+3%]`
The minimum amount of error is contributed by the measurement of a.