In a laboratory experiment the elastic modulus of a metal rod is to be determined…

PHYSICS · Multi-part · A Level · Physics · Measurements and their errors · Measurements and their errors

Problem

In a laboratory experiment the elastic modulus

E

of a metal rod is to be determined from independent measurements of the density

\rho

and the speed

v

of longitudinal waves in the rod. Answer the following: (i) Write the relation connecting

E

v

, and

\rho

for a solid rod. (ii) Derive an expression for the fractional error

\frac{\Delta E}{E}

in terms of the fractional errors

\frac{\Delta v}{v}

and

\frac{\Delta \rho}{\rho}

. (iii) The measurements give

v = (5.00 \pm 0.05) \times 10^3\,\text{m/s}

and

\rho = (7.80 \pm 0.04) \times 10^3\,\text{kg/m}^3

. Calculate the percentage error in the value of

E

obtained from these data.