Elastic Potential Energy in a Stretched Wire
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369915 An elastic material of Young's modulus \(Y\) is subjected to a stress \(S\). The elastic energy stored per unit volume of the material is

1 \(\dfrac{S^{2}}{2 Y}\)
2 \(\dfrac{2 Y}{S^{2}}\)
3 \(\dfrac{S^{2}}{Y}\)
4 \(\dfrac{S}{2 Y}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369916 If in a wire of cross-sectional area \(A\) and length \(l\) and Young's modulus \(Y\), longitudinal strain \(x\) is produced then the potential energy stored in it will be

1 \(0.5 Y^{2} x l\)
2 \(Y x^{2} \mathrm{Al} / 2\)
3 \(Y x^{2} A\)
4 \(2 Y x^{2} A l\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369917 An aluminium rod with Young's modulus \(Y = 7.0 \times {10^{10}}\;N/{m^2}\) undergoes elastic strain of \(0.04 \%\). The energy per unit volume stored in the rod in SI unit is

1 8400
2 11200
3 5600
4 2800
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369918 A copper rod of cross-sectional area \(2\;c{m^2}\) and length \(2{\rm{ }}m\) is compressed length wise by a weight of \(10\;kg\). If young's modulus of elasticity of brass is \({10^{11}}\;N{\rm{/}}{m^2}\) and \(g = 9.8\;m{\rm{/}}{s^2}\) then increase in energy of the rod will be

1 \(480.2\,\,\mu J\)
2 \(490.1\,\,\mu J\)
3 \(1500\,\,\mu J\)
4 None
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PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369915 An elastic material of Young's modulus \(Y\) is subjected to a stress \(S\). The elastic energy stored per unit volume of the material is

1 \(\dfrac{S^{2}}{2 Y}\)
2 \(\dfrac{2 Y}{S^{2}}\)
3 \(\dfrac{S^{2}}{Y}\)
4 \(\dfrac{S}{2 Y}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369916 If in a wire of cross-sectional area \(A\) and length \(l\) and Young's modulus \(Y\), longitudinal strain \(x\) is produced then the potential energy stored in it will be

1 \(0.5 Y^{2} x l\)
2 \(Y x^{2} \mathrm{Al} / 2\)
3 \(Y x^{2} A\)
4 \(2 Y x^{2} A l\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369917 An aluminium rod with Young's modulus \(Y = 7.0 \times {10^{10}}\;N/{m^2}\) undergoes elastic strain of \(0.04 \%\). The energy per unit volume stored in the rod in SI unit is

1 8400
2 11200
3 5600
4 2800
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369918 A copper rod of cross-sectional area \(2\;c{m^2}\) and length \(2{\rm{ }}m\) is compressed length wise by a weight of \(10\;kg\). If young's modulus of elasticity of brass is \({10^{11}}\;N{\rm{/}}{m^2}\) and \(g = 9.8\;m{\rm{/}}{s^2}\) then increase in energy of the rod will be

1 \(480.2\,\,\mu J\)
2 \(490.1\,\,\mu J\)
3 \(1500\,\,\mu J\)
4 None
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369915 An elastic material of Young's modulus \(Y\) is subjected to a stress \(S\). The elastic energy stored per unit volume of the material is

1 \(\dfrac{S^{2}}{2 Y}\)
2 \(\dfrac{2 Y}{S^{2}}\)
3 \(\dfrac{S^{2}}{Y}\)
4 \(\dfrac{S}{2 Y}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369916 If in a wire of cross-sectional area \(A\) and length \(l\) and Young's modulus \(Y\), longitudinal strain \(x\) is produced then the potential energy stored in it will be

1 \(0.5 Y^{2} x l\)
2 \(Y x^{2} \mathrm{Al} / 2\)
3 \(Y x^{2} A\)
4 \(2 Y x^{2} A l\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369917 An aluminium rod with Young's modulus \(Y = 7.0 \times {10^{10}}\;N/{m^2}\) undergoes elastic strain of \(0.04 \%\). The energy per unit volume stored in the rod in SI unit is

1 8400
2 11200
3 5600
4 2800
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369918 A copper rod of cross-sectional area \(2\;c{m^2}\) and length \(2{\rm{ }}m\) is compressed length wise by a weight of \(10\;kg\). If young's modulus of elasticity of brass is \({10^{11}}\;N{\rm{/}}{m^2}\) and \(g = 9.8\;m{\rm{/}}{s^2}\) then increase in energy of the rod will be

1 \(480.2\,\,\mu J\)
2 \(490.1\,\,\mu J\)
3 \(1500\,\,\mu J\)
4 None
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369915 An elastic material of Young's modulus \(Y\) is subjected to a stress \(S\). The elastic energy stored per unit volume of the material is

1 \(\dfrac{S^{2}}{2 Y}\)
2 \(\dfrac{2 Y}{S^{2}}\)
3 \(\dfrac{S^{2}}{Y}\)
4 \(\dfrac{S}{2 Y}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369916 If in a wire of cross-sectional area \(A\) and length \(l\) and Young's modulus \(Y\), longitudinal strain \(x\) is produced then the potential energy stored in it will be

1 \(0.5 Y^{2} x l\)
2 \(Y x^{2} \mathrm{Al} / 2\)
3 \(Y x^{2} A\)
4 \(2 Y x^{2} A l\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369917 An aluminium rod with Young's modulus \(Y = 7.0 \times {10^{10}}\;N/{m^2}\) undergoes elastic strain of \(0.04 \%\). The energy per unit volume stored in the rod in SI unit is

1 8400
2 11200
3 5600
4 2800
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369918 A copper rod of cross-sectional area \(2\;c{m^2}\) and length \(2{\rm{ }}m\) is compressed length wise by a weight of \(10\;kg\). If young's modulus of elasticity of brass is \({10^{11}}\;N{\rm{/}}{m^2}\) and \(g = 9.8\;m{\rm{/}}{s^2}\) then increase in energy of the rod will be

1 \(480.2\,\,\mu J\)
2 \(490.1\,\,\mu J\)
3 \(1500\,\,\mu J\)
4 None