Question

The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively $1.5\%$ and $1\%$, the maximum error in determining the density is?

• A. $2.5\%$
• B. $3.5\%$
• C. $4.5\%$
• D. $6\%$

Answer 1

The correct option is C $4.5\%$

Density $\rho =\frac{m}{V}=\frac{m}{l^3}$
Maximum percentage error in density $\frac{\Delta \rho }{\rho }\times 100=\frac{\Delta m}{m}\times 100+3\frac{\Delta l}{l}\times 100$
$⟹$ $\frac{\Delta \rho }{\rho }\times 100=1.5+3\times 1=4.5$%