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Ratio of extensions of wires when length, radius or force change

This type of question, asked 6 times: 25 Jul 2022, 30 Jan 2023, 10 Apr 2023, 15 Apr 2023, 29 Jan 2024, 7 Apr 2025. All 7 questions 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

    30 Jan 2023

    107
    A force is applied to a steel wire 'A', rigidly clamped at one end. As a result elongation in the wire is 0.2 mm0.2\text{ }mm. If same force is applied to another steel wire ' BB ' of double the length and a diameter 2.4 times that of the wire 'A', the elongation in the wire ' BB ' will be (wires having uniform circular cross sections)

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  3. Question 3

    10 Apr 2023

    106
    Young's moduli of the material of wires A and B are in the ratio of 1:41:4, while its area of cross sections are in the ratio of 1:31:3. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires AA and BB will be in the ratio of [Assume length of wires A and B are same]

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  4. Question 4

    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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  5. Question 5

    29 Jan 2024

    111
    Two metallic wires PP and QQ have same volume and are made up of same material. If their area of cross sections are in the ratio 4:14:1 and force F1F_{1} is applied to PP, an extension of Δl\Delta l is produced. The force which is required to produce same extension in QQ is F2F_{2}. The value of F1 F2\frac{F_{1}}{{\text{ }F}_{2}} is ______

  6. Question 6

    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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  7. Question 7

    7 Apr 2025

    19
    Two wires AA and BB are made of same material having ratio of lengths LALB=13\frac{L_{A}}{L_{B}}=\frac{1}{3} and their diameters ratio dAdB=2\frac{d_{A}}{d_{B}}= 2. If both the wires are stretched using same force, what would be the ratio of their respective elongations?

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