Question

The mass and density of the solid sphere are measured to be $(12.4\pm 0.1)kg$ and $(4.6\pm 0.2)kg/m^3$. Find its volume.

Answer 1

Here, $m\pm \Delta m=(12.4\pm 0.1)kg$
and $\rho \pm \Delta \rho =(4.6\pm 0.2)kg/m^3$
Volume $V=\frac{m}{\rho }=\frac{12.4}{4.6}$
$=2.69m^3=2.7m^3$ (Rounding off to one decimal place)
Now, $\frac{\Delta V}{V}=\pm (\frac{\Delta m}{m}+\frac{\Delta \rho }{\rho })$
or $\Delta V=\pm (\frac{\Delta m}{m}+\frac{\Delta \rho }{\rho })\times V$
$=\pm (\frac{0.1}{12.4}+\frac{0.2}{4.6})\times 27=\pm 0.14\therefore V\pm \Delta V=(2.7\pm 0.14)m^3$