Source: Extra Practice

A physical quantity PP is related to four observables a,b,ca, b, c and dd as P=a3b2cdP = \frac{a^3 b^2}{\sqrt{c} d}. The percentage errors of measurement in a,b,ca, b, c and dd are 1%,3%,4%1\%, 3\%, 4\% and 2%2\% respectively. Calculate the maximum percentage error in the quantity PP.

Options

Option A is correct

13%

Option B

7%

Option C

10%

Option D

14%

Explanation

To find the maximum percentage error in a product/quotient involving powers, we use the formula: ΔPP=3Δaa+2Δbb+12Δcc+Δdd\frac{\Delta P}{P} = 3\frac{\Delta a}{a} + 2\frac{\Delta b}{b} + \frac{1}{2}\frac{\Delta c}{c} + \frac{\Delta d}{d}. Note that errors always add up to find the 'maximum' possible error, and constants or denominators are treated with positive coefficients. Substituting the given percentage errors: Percentage error in P=3(1%)+2(3%)+0.5(4%)+1(2%)=3%+6%+2%+2%=13%P = 3(1\%) + 2(3\%) + 0.5(4\%) + 1(2\%) = 3\% + 6\% + 2\% + 2\% = 13\%. Therefore, 13% is the correct answer. The other options are incorrect as they result from arithmetic mistakes or failing to multiply by the correct exponents.