Question

The density of the material of a cube can be estimated by measuring its mass and the length of one of its sides. If the maximum error in the measurement of mass and length are 0.3% and 0.2% respectively, the maximum error in the estimation of the density of the cube is approximately

• A. 0.011
• B. 0.005
• C. 0.009
• D. 0.007

Answer 1

The Correct Option is C

$Density \left(\rho\right)= =\frac{Mass \left(m\right)}{Volume \left(V\right)}$
$\therefore\left(\frac{\bigtriangleup\rho}{\rho}\right)_{max} =\frac{\bigtriangleup m}{m}+\frac{\Delta v}{v}=\frac{\Delta m}{m}+\frac{3\Delta L}{L}$
$V = L^{3}$
$\left[\because\frac{\Delta V}{V}= \frac{3\Delta L}{L}\right]$
$\therefore\left(\frac{\Delta\rho}{\rho}\right)_{max} \times100 =\lfloor0.3+3\left(0.2\right)\rfloor\%_{=0.9\%}$