A wire of Young's modulus $1 \cdot 6 \times 10^{12} \mathrm{~N} / \mathrm{m}^{2}$ is stretched by a force so…

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
  1. $3 \cdot 2 \times 10^{4} \mathrm{~J} / \mathrm{m}^{3}$
  2. $3 \cdot 2 \times 10^{8} \mathrm{~J} / \mathrm{m}^{3}$
  3. $1 \cdot 6 \times 10^{3} \mathrm{~J} / \mathrm{m}^{3}$
  4. $6 \cdot 4 \times 10^{3} \mathrm{~J} / \mathrm{m}^{3}$

Solution

Energy $=1 / 2 \times Y \times(\text { Strain })^{2}$ $=1 / 2 \times 1.6 \times 10^{12} \times 4^{2} \times 10^{-8}$ $=3.2 \times 10^{4}$.

Asked in: MHT CET 2020 (20 Oct Shift 2)

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