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In the density measurement of a cube, the mass and edge length are measured as $(10.00 \pm 0.10)\,\,kg\,$ and $(0.10 \pm 0.01)\,\,m\,$ respectively. The error in the measurement of density is
$0.10\,\,kg/m^3$
$0.31\,\,kg/m^3$
$0.07\,\,kg/m^3$
None of these
Solution
$\begin{array}{l} \rho = \frac{m}{v}\\ Maximum\,\% \,error\,in\,\rho \,will\,be\,given\,by\\ \frac{{\Delta p}}{p} \times 100\% = \left( {\frac{{\Delta m}}{m}} \right) \times 100\% + 3\left( {\frac{{\Delta L}}{L}} \right) \times 100\% \,\,…\left( i \right)\\ This\,is\,not\,applicable\,as\,error\,is\,big. \end{array}$
$\begin{array}{l} {\rho _{\min }} = \frac{{{m_{\min }}}}{{{v_{\max }}}} = \frac{{9.9}}{{{{\left( {0.11} \right)}^3}}} = 7438kg/{m^3}\\ and \,{\rho _{\max \,}} = \frac{{{m_{\max }}}}{{{v_{\min }}}} = \frac{{10.1}}{{{{\left( {0.09} \right)}^3}}} = 13854.6kg/{m^3}\\ \Delta \rho = 6416.6\,\,kg/{m^3}\\ \end{array}$
