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  4. In the density measurement of a cube, the mass and edge length are measured as (10.00 ± 0.10) kg and (0.10 ± 0.01) m, respectively. The error in the measurement of density is:

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Q. In the density measurement of a cube, the mass and edge length are measured as $\left(10.00 \pm 0.10\right) \, kg$ and $\left(0.10 \pm 0.01\right) \, m,$ respectively. The error in the measurement of density is:

NTA AbhyasNTA Abhyas 2020Physical World, Units and Measurements

Solution:

Density $\left(\rho \right)=\frac{m a s s}{v o l u m e}$
$\frac{\Delta \rho }{\rho }=\frac{\Delta m}{m}+\frac{\Delta V}{V}$
$=\frac{\Delta m}{m}+\frac{3 \Delta a}{a}$ $\left(\because V = a^{3}\right)$
$=\frac{0.1}{10}+3\left(\frac{0.01}{0.1}\right)$
$=0.01+3\left(0.1\right)$
$=0.31$