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Units and Measurement question

2023 · Q140
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Units and Measurement question

2023 · Q140

NEETPhysicsUnits and MeasurementMCQ+4 / −1

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

  1. A
    1.3%
  2. B
    1.6%
  3. C
    1.4%
  4. D
    1.2%
View written solutionFree

Correct answer: B

$\rho=\frac{M}{V}$

$$\rho=\frac{M}{\pi r^{2} \ell}$$

$$\frac{\Delta \rho}{\rho}=\frac{\Delta \mathrm{M}}{\mathrm{M}}+\frac{2 \Delta \mathrm{r}}{\mathrm{r}}+\frac{\Delta \ell}{\ell}$$

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

$$=\frac{1}{2} \%+\frac{2}{3} \%+\frac{2}{5} \%$$

$=1.6 \%$

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