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Question: Answered & Verified by Expert
A wire of Young's modulus $1 \cdot 6 \times 10^{12} \mathrm{~N} / \mathrm{m}^{2}$ is stretched by a force so as to produce a strain of $2 \times 10^{-4}$. The energy density of the wire is
PhysicsMechanical Properties of SolidsJEE Main
Options:
  • A $3 \cdot 2 \times 10^{4} \mathrm{~J} / \mathrm{m}^{3}$
  • B $3 \cdot 2 \times 10^{8} \mathrm{~J} / \mathrm{m}^{3}$
  • C $1 \cdot 6 \times 10^{3} \mathrm{~J} / \mathrm{m}^{3}$
  • D $6 \cdot 4 \times 10^{3} \mathrm{~J} / \mathrm{m}^{3}$
Solution:
1330 Upvotes Verified Answer
The correct answer is: $3 \cdot 2 \times 10^{4} \mathrm{~J} / \mathrm{m}^{3}$
Energy $=1 / 2 \times Y \times(\text { Strain })^{2}$
$=1 / 2 \times 1.6 \times 10^{12} \times 4^{2} \times 10^{-8}$
$=3.2 \times 10^{4}$.

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