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Error in Young's modulus from the measured readings

This type of question, asked 4 times: 2021 Paper 24, 26 Jul 2022, 8 Apr 2024, 2 Apr 2026 S1. All 4 questions below, oldest first.

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  1. Question 1

    2021 Paper 24

    8
    A student determined Young's Modulus of elasticity using the formula Y=MgL34bd3δY =\frac{MgL^{3}}{4bd^{3}\delta}. The value of gg is taken to be 9.8 m/s29.8\text{ }m/s^{2}, without any significant error, his observation are as following. Then the fractional error in the measurement of YY is:

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  2. Question 2

    26 Jul 2022

    23
    In an experiment to determine the Young's modulus of wire of a length exactly 1 m1\text{ }m, the extension in the length of the wire is measured as 0.4 mm0.4\text{ }mm with an uncertainty of ±0.02 mm\pm 0.02\text{ }mm when a load of 1 kg1\text{ }kg is applied. The diameter of the wire is measured as 0.4 mm0.4\text{ }mm with an uncertainty of ±0.01 mm\pm 0.01\text{ }mm. The error in the measurement of Young's modulus (ΔY)(\Delta Y) is found to be x×1010Nm−2x \times10^{10}Nm^{- 2}. The value of xx is [Take g=10 m/s2g = 10\text{ }m/s^{2} ]

  3. Question 3

    8 Apr 2024

    10
    Young's modulus is determined by the equation given by Y=49000Mldynecm2Y = 49000\frac{M}{\mathcal{l}}\frac{dyne}{cm^{2}} where MM is the mass and l\mathcal{l} is the extension of wire used in the experiment. Now error in Young's modulus (Y) is estimated by taking data from M−lM -\mathcal{l} plot in graph paper. The smallest scale divisions are 5 g5\text{ }g and 0.02 cmcm along load axis and extension axis respectively. If the value of MM and l\mathcal{l} are 500 g500\text{ }g and 2 cm2\text{ }cm respectively then percentage error of YY is:

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  4. Question 4

    2 Apr 2026 S1

    2
    The diameter of a wire measured by a screw gauge of least count 0.001 cm is 0.08 cm . The length measured by a scale of least count 0.1 cm is 150 cm . When a weight of 100 N is applied to the wire, the extension in length is 0.5 cm , measured by a micrometer of least count 0.001 cm . The error in the measured Young's modulus is α×109 N/m2\alpha \times10^{9}\text{ }N/m^{2}. The value of α\alpha is ____\_\_\_\_.(Ignore the contribution of the load to Young's modulus error calculation)

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