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. $\pm 0.03c{m}^3$
• B. $\pm 0.111c{m}^3$
• C. $\pm 0.012c{m}^3$
• D. none of these

Answer 1

Answer: (A)

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