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

Correct answer: (D) 1.6%. Density=mass/volume ⇒ρ=m/(πr^2l) Therefore, percentage error can be written as ⇒(dρ)/(ρ)×100=dm/m+2dr/r+dl/l×100=0.002/0.4+20.001/0.3+0.02/5×100≈1.6%

Q100 / 200 · NEET 2023 (All India) · Physics

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
$1.4 %$
B
$1.2 %$
C
$1.3 %$
Correct answer
D
$1.6 %$

Solution

Density $= \frac{mass}{volume}$
$\Rightarrow ρ = \frac{m}{π r^{2} l}$
Therefore, percentage error can be written as
$\Rightarrow \frac{d ρ}{ρ} \times 100 = [\frac{d m}{m} + 2 (\frac{d r}{r}) + \frac{d l}{l}] \times 100 = [\frac{0.002}{0.4} + 2 (\frac{0.001}{0.3}) + \frac{0.02}{5}] \times 100 \approx 1.6 %$

Hence, the correct answer is option: 'D'.

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