JEE MAIN - Physics (2005 - No. 29)
If $$S$$ is stress and $$Y$$ is young's modulus of material of a wire, the energy stored in the wire per unit volume is
$${{{S^2}} \over {2Y}}$$
$$2{S^2}Y$$
$${S \over {2Y}}$$
$${{2Y} \over {{S^2}}}$$
Giải thích
Energy stored per unit volume of wire,
$$E = {1 \over 2} \times \,stress\, \times \,strain$$
$$\therefore$$ $$E = {1 \over 2} \times \,stress\, \times \,{{stress} \over Y} = {1 \over 2}{{{S^2}} \over Y}$$
[ As Young's modulus(Y) = $${{Stress} \over {Strain}}$$
$$\therefore$$ Strain = $${{Stress} \over Y}$$ ]
$$E = {1 \over 2} \times \,stress\, \times \,strain$$
$$\therefore$$ $$E = {1 \over 2} \times \,stress\, \times \,{{stress} \over Y} = {1 \over 2}{{{S^2}} \over Y}$$
[ As Young's modulus(Y) = $${{Stress} \over {Strain}}$$
$$\therefore$$ Strain = $${{Stress} \over Y}$$ ]