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  4. The density of a cube is measured by measuring its mass and the length of its side. If the maximum errors in the measurement of mass and length are 4 % and 3 %, respectively, then the maximum error in the measurement of the density is

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Q. The density of a cube is measured by measuring its mass and the length of its side. If the maximum errors in the measurement of mass and length are $4\%$ and $3\%$, respectively, then the maximum error in the measurement of the density is

Physical World, Units and Measurements

Solution:

Density $\left(\rho\right)=\frac{Mass}{Volume}=\frac{m}{l^{3}}$
$\frac{\Delta\rho}{\rho}\times100=\frac{\Delta m}{m}\times100+3 \frac{\Delta l}{l}\times100$
$=4\%+3\times3\%=13\%$