A wire has a mass g, radius cm and length cm. What is the maximum percentage error in the measurement of density?

JEE MainPhysicsModerateError analysis

A wire has a mass $0.3\ \pm \ 0.003$ g, radius
$0.5\ 0 \pm 0.005$ cm and length $6 \pm 0.06$ cm. What is the maximum
percentage error in the measurement of density?

Show answer and solution

\frac{d\rho}{A} = \frac{dm}{m} + 2\frac{dr}{r} + \frac{dl}{l}

\%\frac{d\rho}{A} = \left( \frac{0.003}{0.3} + 2*\frac{0.005}{0.5} + \frac{0.06}{6} \right)*100 = 4\%

Source: Grass-G / P-05 Physics paper 10 October.docx

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