Physics

Problem

Consider two independent measured quantities:

\;a = 3.00 \pm 0.05\,

(no unit specified) and

\;b = 4.00 \pm 0.10

. A derived quantity is defined as

Q = (a\,b^{2})^{1/3}

. (i) Derive an expression for the fractional uncertainty

\displaystyle \frac{\Delta Q}{Q}

in terms of

\displaystyle \frac{\Delta a}{a}

and

\displaystyle \frac{\Delta b}{b}

. (ii) Using the given data, calculate the numerical value of

Q

and its absolute uncertainty

\Delta Q

. (iii) State the final result for

Q

with its uncertainty to an appropriate number of significant figures.