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  • A metal wire has mass , radius <img alt="(0.3 \pm 0.001) \mathrm{mm}" src="https:/

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

Option: 1

1.2 \%


Option: 2

1.3 \%


Option: 3

1.6 \%


Option: 4

1.4 \%


Answers (1)

best_answer

\begin{aligned} & \rho=\frac{\text { Volume }}{\text { Vos }}=\frac{\mathrm{m}}{\pi r^2 \ell} \\ & \frac{\Delta \mathrm{m}}{\mathrm{m}} \times 100=\frac{0.002}{0.4} \times 100=0.5 \% \\ & \frac{\Delta \mathrm{r}}{\mathrm{r}} \times 100=\frac{0.001}{0.3} \times 100=\frac{1}{3} \% \end{aligned}

\begin{aligned} & \frac{\Delta \ell}{\ell} \times 100=\frac{0.02}{5} \times 100=0.4 \% \\ & \frac{\Delta \rho}{\rho} \times 100=\left(\frac{\Delta \mathrm{m}}{\mathrm{m}} \times 100\right)+2 \frac{\Delta \mathrm{r}}{\mathrm{r}} \times 100+\frac{\Delta \ell}{\ell} \times 100 \\ & =1.56 \% \\ & \simeq 1.6 \% \end{aligned}

Posted by

rishi.raj

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