Question

A wire of length$l=6\pm 0.06cm$ and radius $r=0.5\pm 0.005cm$ and mass $m=0.3\pm 0.03gm$. Maximum percentage error in density is.

• A. $4$
• B. $2$
• C. $1$
• D. $6.8$

Answer 1

The correct option is A

$4$

Step 1: Given data.

The length of the wire is $l=6\pm 0.06cm$

Radius $r=0.5\pm 0.005cm$

Mass $m=0.3\pm 0.03gm$

Step 2: Calculating maximum percentage error in density ($\rho$).

We know density is given as $\rho =\frac{m}{\pi r^{2}l}$

Where $m$ is the mass

$r$ is the radius

$l$ is the length of wire

Therefore, the percentage error is calculated as below,

$$\begin{gathered} \left(\frac{∆\rho }{\rho }\right)\times 100=\left(\frac{∆m}{m}+\frac{2∆r}{r}+\frac{∆l}{l}\right)\times 100 \\ =\left(\frac{0.003}{0.3}+\frac{2\times 0.005}{0.5}+\frac{0.06}{6}\right)\times 100 \\ =\left(0.01+0.02+0.01\right)\times 100 \\ =4\% \end{gathered}$$

Hence, the correct option is (A).