NEET 2023, Physics Q14: Measurements

NEET2023Physics

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:

A
$1.3%$
B
$1.6%$
C
$1.4%$
D
$1.2%$

Solution

Density $ρ = \frac{M}{π r ^{2} L}$ . Maximum fractional error adds:

$\frac{Δ ρ}{ρ} = \frac{Δ M}{M} + 2 \frac{Δ r}{r} + \frac{Δ L}{L}$

$= \frac{0.002}{0.4} + 2 \times \frac{0.001}{0.3} + \frac{0.02}{5}$

$= 0.005 + 0.00667 + 0.004 \approx 0.0157 \approx 1.6%$ .

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NEET 2023, Physics Q14: Measurements

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