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Mathematics in Physics

JEE Main level, single correct, medium

92 of 121

Question 92 of 121

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

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Answer: (D) $1.4%$

Y=\dfrac{Stress}{Strain}=\dfrac{FL}{Al}=\dfrac{mgL}{\pi {R}^{2}l}

\dfrac{\Delta Y}{Y}=\dfrac{\Delta m}{m}+\dfrac{\Delta L}{L}+2\dfrac{\Delta R}{R}+\dfrac{\Delta l}{l}

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

=\dfrac{1}{10}+\dfrac{1}{10}+1+\dfrac{1}{5}=\dfrac{14}{10}=1.4%

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