Answer to Question #102108 in Mechanics | Relativity for Ibi

Question

Stewart Dent is asked to measure the density of a piece of iron. He measures the mass of the iron and records a value of 97.4g. He measures the volume of water in a graduated cylinder as 50.4mL, after submerging the iron , the volume is 63.3mL .if tje actual density of iron is 7.874g/mL what is Stewart's %-error?

Answer 1

Calculated value of density:

${\rho}_{approx} = \cfrac m V = \cfrac m {V_1 - V_0} ,$

where

$\qquad m$ - measured mass of the iron

$\qquad V_0$ - volume of water in a graduated cylinder before submerging the iron

$\qquad V_1$ - volume of water in a graduated cylinder after submerging the iron

${\rho}_{approx} = \cfrac {97.4} {63.3 - 50.4} \approx 7.6 \text{ (g/mL)}$

Stewart's %-error (relative error):

$\delta = \Big| \cfrac {\rho - {{\rho}_{approx}}} \rho \Big| * 100\% = \Big| 1 - \cfrac {{\rho}_{approx}} \rho \Big| * 100\% = \Big| 1 - \cfrac {7.6} {7.874} \Big| * 100\% \approx 3.5\%$