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

Physics · Units, Dimensions & Error Analysis

NEET (UG) 2023 — Question 14

A metal wire has mass $(0.4 \pm 0.002) \mathrm{g}$ , 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 A:
$1.3 \%$
Option B:
$1.6 \%$
Correct
Option C:
$1.4 \%$
Option D:
$1.2 \%$

Answer: B

Step-by-step solution

\text { We know, } \rho=\frac{\text { Mass }}{\text { Volume }}=\frac{M}{\pi r^2 \ell}

Using the concept of errors we know,

\begin{aligned} & \frac{\Delta \rho}{\rho}=\frac{\Delta M}{M}+\frac{2 \Delta r}{r}+\frac{\Delta \ell}{\ell} \\ & =\left(\frac{0.002}{0.4}+\frac{2 \times 0.001}{0.3}+\frac{0.02}{5}\right) \end{aligned}

\begin{aligned} & \frac{\Delta \rho}{\rho}=0.0156 \\ & \frac{\Delta \rho}{\rho} \%=1.56 \% \approx 1.6 \% \end{aligned}

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Exam: NEET (UG) 2023
Paper: 2023 paper
Subject: Physics
Chapter: Units, Dimensions & Error Analysis
Topic: Significant Figures and Error Analysis

Answer: B

Step-by-step solution

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