Question

The length, breadth and thickness of a strip are $(10.0\,\pm \, 0.1) \,cm$, $(1.00\, \pm \, 0.01)\, cm$ and $(0.100\, \pm \,0.001)\,cm$, respectively, then the most probable error in its volume will be

• A. $\pm 0.03\,cm^3$
• B. $\pm 0.111\,cm^3$
• C. $\pm 0.012\,cm^3$
• D. none of these

Answer 1

Answer: (A)

$V =$ Length $\times$ Width $\times$ Thickness
$\frac{\Delta V}{V}=\pm\frac{\Delta l}{l}\pm\frac{\Delta w}{w}\pm\frac{\Delta t}{t}$
$=\pm\frac{0.1}{10}\pm\frac{0.01}{1}\pm\frac{0.001}{0.1}$
$=\left(\pm\,0.01\,\pm\,0.01\,\pm\,0.01\right)$
$=\pm\,0.03\,cm^{3}$