Question

A wire has a mass $0.3 \, \pm0.003 \, g,$ radius $0.5 \, \pm0.005 \, mm$ and length $6 \, \pm0.06 \, cm.$ The maximum percentage error in the measurement of its density is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (D)

Density
$\rho =\frac{m}{\pi r^{2} L}$
$\therefore \frac{\Delta \rho }{\rho }\times 100=\left(\frac{\Delta m}{m} + 2 \frac{\Delta r}{r} + \frac{\Delta L}{L}\right)\times 100$
After substituting the values we get the maximum percentage error in density $= 4\%$