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Properties of Matter question

2023 · Q142
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Properties of Matter question

2023 · Q142

NEETPhysicsProperties of MatterMCQ+4 / −1

The amount of elastic potential energy per unit volume (in SI unit) of a steel wire of length 100 cm100 \mathrm{~cm}100 cm to stretch it by 1 mm1 \mathrm{~mm}1 mm is (if Young's modulus of the wire =2.0×1011Nm−2=2.0 \times 10^{11} \mathrm{Nm}^{-2}=2.0×1011Nm−2 ) :

  1. A
    101110^{11}1011
  2. B
    101710^{17}1017
  3. C
    10710^7107
  4. D
    10510^5105
View written solutionFree

Correct answer: D

$$ \begin{aligned} & \frac{\text { E.P.E }}{\text { Volume }}=\frac{1}{2}(\text { stress)(strain) } \\ & =\frac{1}{2}(Y)(\text { strain })^2 \\ & =\frac{1}{2}(\mathrm{Y})\left(\frac{\Delta \mathrm{L}}{\mathrm{L}}\right)^2 \\ & =\frac{1}{2}\left(2 \times 10^{11}\right)\left(\frac{1 \times 10^{-3}}{100 \times 10^{-2}}\right)^2 \\ & =10^5 \end{aligned} $$

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