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Extension of two wires joined end to end under one load

This type of question, asked 3 times: 2021 Paper 14, 27 Jul 2022, 4 Apr 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    2021 Paper 14

    11
    Two wires of equal dimensions and Young's modulus Y1Y_{1} and Y2Y_{2} are connected end to end. What is the equivalent Young's modulus for the combination?

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  2. Question 2

    27 Jul 2022

    97
    A steel wire of length 3.2 m(YS=2.0×1011Nm−2)3.2\text{ }m\left( Y_{S}= 2.0 \times10^{11}Nm^{- 2} \right) and a copper wire of length 4.4 m4.4\text{ }m (YC=1.1×1011Nm−2)\left( Y_{C}= 1.1 \times10^{11}Nm^{- 2} \right), both of radius 1.4 mm1.4\text{ }mm are connected end to end. When stretched by a load, the net elongation is found to be 1.4 mm1.4\text{ }mm. The load applied, in Newton, will be: (Given π=227\pi =\frac{22}{7} )

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  3. Question 3

    4 Apr 2026 S1

    9
    A string A of length 0.314 m of Young's modulus 2×1010 N/m22 \times10^{10}\text{ }N/m^{2} is connected to another string B of length and Young's modulus both twice of those of A. This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass 0.8 kg . The net change in length of the combination is ____\_\_\_\_ mm . (radius of both the strings is 0.2 mm and acceleration due to gravity =10 m/s2= 10\text{ }m/s^{2} ) (Mass of both strings is to be neglected as compared to the mass of load)

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