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  4. The density of the 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 3.5 % and 1 %, then the maximum error in determining the density is %.

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Q. The density of the 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 $3.5 \%$ and $1 \%$, then the maximum error in determining the density is___________$\%$.

Physical World, Units and Measurements

Solution:

Density $(\rho)=\frac{\text { Mass }}{\text { Volume }}=\frac{ m }{l^{3}} ....\left(\right.$ for cube $\left.V =l^{3}\right)$
Percentage relative error in density will be,
$\frac{\Delta \rho}{\rho} \times 100 =\left[\frac{\Delta m }{ m }+3 \frac{\Delta l}{l}\right] \%$
$=[3.5+(3 \times 1)] \%$
$=(3.5+3) \%=6.5 \%$