Question

A metal wire has mass (0.4±0.002)g, radius (0.3±0.001)mm and length (5±0.02)cm. The maximum possible percentage error in the measurement of density will nearly be:

• A. 1.4%
• B. 1.2%
• C. 1.3%
• D. 1.6%

Answer 1

The Correct Option is D

We know that,
\(\rho =  \frac{M}{V}\)

\(\rho= \frac{M}{\pi r^2l}\)

\(\frac{\Delta\rho}{\rho}= \frac{\Delta M}{M}+ \frac{2\Delta r}{r}+ \frac{\Delta l}{l}\)

\(\frac{\Delta\rho}{\rho}\)% = [\(\frac{0.002}{0.4}+ \frac{2(0.001)}{0.3}+ \frac{0.02}{5}\)]\(\times 100\)

\(\frac{\Delta\rho}{\rho}\)% \(= \frac{1}{2}\)%+\(\frac{2}{3}\)%+\(\frac{2}{5}\)%

\(\frac{\Delta\rho}{\rho}\)% = 1.6%

So, the correct option is (D): 1.60%