A cylinder’s density is to be found using

PHYSICS · Subjective · A Level · Physics · Measurements and their errors · Measurements and their errors

Problem

\rho=\dfrac{m}{\pi r^{2}h}

. The measured values are

m=100.0\,\text{g}\,\pm1.0\,\text{g}

r=2.00\,\text{cm}\,\pm0.01\,\text{cm}

and

h=10.0\,\text{cm}\,\pm0.1\,\text{cm}

. Without performing a full calculation, state which single measurement (

m,\,r

h

) should be improved first to obtain the greatest reduction in the percentage uncertainty in

\rho

, and give one brief reason.