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:

1. 1.4%

2. 1.2%

3. 1.3%

4. 1.6%

Doubtly Asked 30 Oct 2026 NEET UG 2023 Practice test neet Save WhatsApp Report

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Answer: 4. 1.6%

Density \(\rho=\dfrac{m}{\pi r^2 l}\). The maximum fractional errors add, with the radius error counted twice because of \(r^2\).

\(\dfrac{\Delta\rho}{\rho}=\dfrac{\Delta m}{m}+2\dfrac{\Delta r}{r}+\dfrac{\Delta l}{l}\)

\(=\dfrac{0.002}{0.4}+2\times\dfrac{0.001}{0.3}+\dfrac{0.02}{5}=0.5\%+0.67\%+0.4\%\approx1.6\%\).

The answer is 1.6%.

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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