Q. A wire has a mass $0.3\ \pm 0.003\ g,$ radius $0.5\ \pm 0.005\ mm$ 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
Explanation
Density $\rho = \frac{m}{\pi r^{2}L}$ $\therefore\frac{\mathrm{\Delta}\rho}{\rho} \times 100 = \left( \frac{\mathrm{\Delta}m}{m} + 2\frac{\mathrm{\Delta}r}{r} + \frac{\mathrm{\Delta}L}{L} \right) \times 100$ After substituting the values we get the maximum percentage error in density =4%
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.