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Elastic potential energy or energy density stored in a stretched wire

This type of question, asked 6 times: 2021 Paper 16, 26 Jun 2022, 8 Apr 2023, 13 Apr 2023, 2 Apr 2025, 5 Apr 2026 S2. All 6 questions below, oldest first.

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  1. Question 1

    2021 Paper 16

    12
    Young's modulus of a string is 0.5×109 Pa0.5 \times10^{9}\text{ }Pa, length of the wire without any force applied is 0.1 m0.1\text{ }m and area is 0.04×10−4 m20.04 \times10^{- 4}{\text{ }m}^{2}. If this wire is stretched by a length of 0.001 m0.001\text{ }m. The energy stored in this string is transferred to a particle of mass 20 grams. Find speed of the particle.

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  2. Question 2

    26 Jun 2022

    23
    The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of 5×10−45 \times10^{- 4} is ____ kJ/m3\_\_\_\_\ kJ/m^{3}. Assume that material is elastic upto the linear strain of 5×10−45 \times10^{- 4}.

  3. Question 3

    8 Apr 2023

    8
    An aluminium rod with Young's modulus Y=7.0Y = 7.0 ×1010 N/m2\times10^{10}\text{ }N/m^{2} undergoes elastic strain of 0.04%0.04\%. The energy per unit volume stored in the rod in SI unit is:

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  4. Question 4

    13 Apr 2023

    21
    The elastic potential energy stored in a steel wire of length 20 m20\text{ }m stretched through 2 cm2\text{ }cm is 80 J80\text{ }J. The cross-sectional area of the wire is ___ mm2mm^{2}. (Given, y=2.0×1011Nm−2y = 2.0 \times10^{11}Nm^{- 2} )

  5. Question 5

    2 Apr 2025

    22
    A steel wire of length 2 m and Young's modulus 2.0×1011Nm−22.0 \times 10^{11}{Nm}^{- 2} is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and 10−310^{- 3} respectively, then the elastic potential energy density of the wire is α×105\alpha \times 10^{5} (in SI units). The value of α\alpha is ____\_\_\_\_.

  6. Question 6

    5 Apr 2026 S2

    21
    A copper wire of length 3 m is stretched by 3 mm by applying an external force. The volume of the wire is 600×10−6 m3600 \times 10^{- 6}{\text{ }m}^{3}. The elastic potential energy stored in the wire in stretched condition would be ____\_\_\_\_ J. (Given Young modulus of copper  =1.1×1011 N/m2)\left. \ = 1.1 \times 10^{11}\text{ }N/m^{2} \right)