Question

The density of a sphere is measured by measuring the mass and diameter. If it is known that the maximum percentage errors in the measurement of mass and diameter are $2\%$ and $3\%$ respectively then the maximum percentage error in the measurement of density is

Answer 1

Answer: 11

The density can be computed by
$\rho =\frac{m}{v}=\frac{\frac{m}{\pi d^3}}{6}$
or $\rho \propto \frac{m}{\pi d^3}$
$\therefore \frac{\Delta \rho }{\rho }\times 100\%=\frac{\Delta m}{m}\times 100\%+3\frac{\Delta d}{d}\times 100\%$
or $\frac{\Delta \rho }{\rho }\times 100=2+3\times 3=11$
Hence, the percentage error is measurement of density is $11\%$.