In order to determine the Young's Modulus of a wire of radius \(0.2\, cm\) (measured using a scale of least count \(=0.001\, cm )\) and length \(1 \,m\) (measured using a scale of least count \(=1\, mm\) ), a weight of mass \(1\, kg\) (measured using a scale of least count \(=1 \,g\) ) was hanged to get the elongation of \(0.5\, cm\) (measured using a scale of least count \(0.001\, cm\) ). What will be the fractional error in the value of Young's Modulus determined by this experiment? (in \(\%\))

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Answer & Solution

Correct Answer

(D) \(1.4\)

Detailed explanation

\(Y=\frac{\text { Stress }}{\text { Strain }}=\frac{ FL }{ Al }=\frac{ mg . L }{\pi R ^{2} \cdot \ell}\)

\(\frac{\Delta Y }{ Y }=\frac{\Delta m }{ m }+\frac{\Delta L }{ L }+2 \cdot \frac{\Delta R }{ R }+\frac{\Delta \ell}{\ell}\)

\(\frac{\Delta Y }{ Y } \times 100=100\left[\frac{1}{1000}+\frac{1}{1000}+2\left(\frac{0.001}{0.2}\right)+\frac{0.001}{0.5}\right]\)

\(=\frac{1}{10}+\frac{1}{10}+1+\frac{1}{5}=\frac{14}{10}=1.4\, \%\)

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