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Natural length of a wire or spring from its lengths under two different tensions

This type of question, asked 7 times: 2021 Paper 11, 2021 Paper 26, 29 Jun 2022, 11 Apr 2023, 4 Apr 2024, 23 Jan 2025, 2 Apr 2025. All 7 questions below, oldest first.

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  1. Question 1

    2021 Paper 11

    15
    Tension in a spring is T1T_{1} when length of the spring is l1l_{1} and tension is T2T_{2} when its length is l2l_{2}. The natural length of the spring is

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  2. Question 2

    2021 Paper 26

    18
    The length of metallic wire is l1l_{1} when tension in it is T1T_{1}. It is l2l_{2} when the tension is T2T_{2}. The original length of the wire will be:

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  3. Question 3

    29 Jun 2022

    6
    A wire of length LL is hanging from a fixed support. The length changes to L1L_{1} and L2L_{2} when masses 1 kg1\text{ }kg and 2 kg2\text{ }kg are suspended respectively from its free end. Then the value of LL is equal to:

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  4. Question 4

    11 Apr 2023

    27
    The length of wire becomes l1l_{1} and l2l_{2} when 100 N100\text{ }N and 120 N120\text{ }N tensions are applied respectively. If 10l2=11l110l_{2}=11l_{1}, the natural length of wire will be 1xl1\frac{1}{x}l_{1}. Here the value of xx is___
  5. Question 5

    4 Apr 2024

    28
    An elastic spring under tension of 3 N3\text{ }N has a length a. Its length is bb under tension 2 N2\text{ }N. For its length (3a−2b)(3a - 2b), the value of tension will be ____ NN.
  6. Question 6

    23 Jan 2025

    95
    A massless spring gets elongated by amount X1X_{1} under a tension of 5 N . Its elongation is x2x_{2} under the tension of 7 N . For the elongation of (5x1−2x2)\left( 5x_{1}- 2x_{2} \right), the tension in the spring will be,

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  7. Question 7

    2 Apr 2025

    99
    The length of a light string is 1.4 m when the tension on it is 5 N . If the tension increases to 7 N , the length of the string is 1.56 m . The original length of the string is ____\_\_\_\_ m.