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Wire of length L and radius r extends by l under force F: extension when length, radius and force are scaled

The same question, asked 3 times: 25 Jul 2022*, 15 Apr 2023*, 29 Jan 2024. Every wording below, oldest first.

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  1. Question 1

    25 Jul 2022

    23
    A wire of length LL and radius rr is clamped rigidly at one end. When the other end of the wire is pulled by a force FF, its length increases by 5 cm5\text{ }cm. Another wire of the same material of length 4 L4\text{ }L and radius 4r4r is pulled by a force 4 F4\text{ }F under same conditions. The increase in length of this wire is ____\_\_\_\_ cm.
  2. Question 2

    15 Apr 2023

    12
    A wire of length ' LL ' and radius ' rr ' is clamped rigidly at one end. When the other end of the wire is pulled by a force ff, its length increases by ' l\mathcal{l} '. Another wire of same material of length ' 2L2L ' and radius ' 2r2r ' is pulled by a force ' 2f2f '. Then the increase in its length will be:

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  3. Question 3

    29 Jan 2024

    103
    A wire of length LL and radius rr is clamped at one end. If its other end is pulled by a force F, its length increases by ll. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become.

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