In order to determine the Young's Modulus of a wire of radius 0.2 cm… | JEE Main 2021 (16 Mar, Shift 2)

Q87JEE Main 2021 · 16 MAR · SHIFT 2Difficult

Errors in Measurement

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 1m (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?

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Answer: (c)

$Y = \dfrac{mgL}{\pi r^2\,\Delta l}$ , so $\dfrac{\Delta Y}{Y} = \dfrac{\Delta m}{m} + \dfrac{\Delta L}{L} + 2\dfrac{\Delta r}{r} + \dfrac{\delta(\Delta l)}{\Delta l}$ .
$\dfrac{1}{1000} + \dfrac{1}{1000} + 2\times\dfrac{0.001}{0.2} + \dfrac{0.001}{0.5}$
$= 0.1\% + 0.1\% + 1\% + 0.2\% = 1.4\%$
So the answer is (c) $1.4\%$ .

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Errors in Measurement question from JEE Main 2021 (16 Mar, Shift 2)

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