Question

A wire has a mass $(0.3 \pm 0.003)\, g$, radius $(0.5 \pm 0.005)\,cm$ and length $(6 \pm 0.06) \,cm$. The maximum percentage error in the measurement of its density is

• A. $1\%$
• B. $2\%$
• C. $3\%$
• D. $4\%$

Answer 1

Answer: (D)

Density $\left(\rho\right)=\frac{m}{\pi r^{2}l}$
$\therefore \left(\frac{\Delta\rho}{\rho}\right)\times100=\left(\frac{\Delta m}{m}+2\times\frac{\Delta r}{r}+\frac{\Delta l}{l}\right)\times100$
$=\left(\frac{0.003}{0.3}+2\times\frac{0.005}{0.5}+\frac{0.06}{6}\right)\times100$
$=\left(0.01+0.02+0.01\right)\times100$
$=4\%$