Thermal Expansion
PHXI11:THERMAL PROPERTIES OF MATTER

366729 A bimetallic strip is made of aluminium and steel \(\left(\alpha_{A l}>\alpha_{\text {steel }}\right)\). On heating, the strip will

1 Remain straight
2 Get twisted
3 Will bend with aluminium on concave side
4 Will bend with steel on concave side
PHXI11:THERMAL PROPERTIES OF MATTER

366730 An iron bar of length \(10\;m\) is heated from \(0^\circ C\) to \(100^\circ C\). If the coefficient of linear thermal expansion of iron is \(10 \times 10^{-6} /{ }^{\circ} \mathrm{C}\), the increase in the length of bar is

1 \(0.5\;cm\)
2 \(1.0\;cm\)
3 \(1.5\;cm\)
4 \(2.0\;cm\)
PHXI11:THERMAL PROPERTIES OF MATTER

366731 The material whose elasticity remains constant even when the temperature is changed is

1 Bimetallic strip
2 Aluminum
3 Invar steel
4 Alnico
PHXI11:THERMAL PROPERTIES OF MATTER

366732 A rail track made of steel having length \(10\;cm\) is clamped on a railway line at its two ends (figure). On a summer day due to rise in temperature by \(20^\circ C\). It is deformed as shown in figure. Find \(x\) (displacement of the centre) if \({\alpha _{{\rm{steel }}}} = 1.2 \times {10^{ - 5}}/^\circ C\)
supporting img

1 \(15\sqrt {30} \times {10^{ - 3}}\;cm\)
2 \(20\sqrt {30} \times {10^{ - 3}}\;cm\)
3 \(25\sqrt {30} \times {10^{ - 3}}\;cm\)
4 \(10\sqrt {30} \times {10^{ - 3}}\;cm\)
PHXI11:THERMAL PROPERTIES OF MATTER

366733 Two steel rods and an aluminium rod of length \(l_{0}\) and equal cross section are joined rigidly at their eand as shown in the figure below. All the rods are in a state of zero tension at \(0^\circ C\). Find the length of the system when the temperature is raised to \(\Delta T\). Coefficient of linear expansion of aluminium and steel are \(\alpha_{a}\) and \(\alpha_{s}\) respectively. Young's modulus of aluminium and steel are \(Y_{a}\) and \(Y_{s}\) respectively \(\left(\alpha_{s}>\alpha_{a}\right)\).
supporting img

1 \(l_{0} \Delta T\left[\alpha_{s}+\alpha_{a}\right]\)
2 \(\dfrac{l_{0} \Delta T\left[2 Y_{s} \alpha_{s}+Y_{a} \alpha_{a}\right]}{\left[Y_{a}+2 Y_{s}\right]}\)
3 \(\dfrac{l_{0} \Delta T\left[Y_{s} \alpha_{s}+Y_{a} \alpha_{a}\right]}{\left[Y_{a}+Y_{s}\right]}\)
4 \(\dfrac{l_{0} \Delta T\left[2 \alpha_{s}+\alpha_{a}\right] Y_{s} Y_{a}}{\left[Y_{a}+Y_{s}\right]}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366729 A bimetallic strip is made of aluminium and steel \(\left(\alpha_{A l}>\alpha_{\text {steel }}\right)\). On heating, the strip will

1 Remain straight
2 Get twisted
3 Will bend with aluminium on concave side
4 Will bend with steel on concave side
PHXI11:THERMAL PROPERTIES OF MATTER

366730 An iron bar of length \(10\;m\) is heated from \(0^\circ C\) to \(100^\circ C\). If the coefficient of linear thermal expansion of iron is \(10 \times 10^{-6} /{ }^{\circ} \mathrm{C}\), the increase in the length of bar is

1 \(0.5\;cm\)
2 \(1.0\;cm\)
3 \(1.5\;cm\)
4 \(2.0\;cm\)
PHXI11:THERMAL PROPERTIES OF MATTER

366731 The material whose elasticity remains constant even when the temperature is changed is

1 Bimetallic strip
2 Aluminum
3 Invar steel
4 Alnico
PHXI11:THERMAL PROPERTIES OF MATTER

366732 A rail track made of steel having length \(10\;cm\) is clamped on a railway line at its two ends (figure). On a summer day due to rise in temperature by \(20^\circ C\). It is deformed as shown in figure. Find \(x\) (displacement of the centre) if \({\alpha _{{\rm{steel }}}} = 1.2 \times {10^{ - 5}}/^\circ C\)
supporting img

1 \(15\sqrt {30} \times {10^{ - 3}}\;cm\)
2 \(20\sqrt {30} \times {10^{ - 3}}\;cm\)
3 \(25\sqrt {30} \times {10^{ - 3}}\;cm\)
4 \(10\sqrt {30} \times {10^{ - 3}}\;cm\)
PHXI11:THERMAL PROPERTIES OF MATTER

366733 Two steel rods and an aluminium rod of length \(l_{0}\) and equal cross section are joined rigidly at their eand as shown in the figure below. All the rods are in a state of zero tension at \(0^\circ C\). Find the length of the system when the temperature is raised to \(\Delta T\). Coefficient of linear expansion of aluminium and steel are \(\alpha_{a}\) and \(\alpha_{s}\) respectively. Young's modulus of aluminium and steel are \(Y_{a}\) and \(Y_{s}\) respectively \(\left(\alpha_{s}>\alpha_{a}\right)\).
supporting img

1 \(l_{0} \Delta T\left[\alpha_{s}+\alpha_{a}\right]\)
2 \(\dfrac{l_{0} \Delta T\left[2 Y_{s} \alpha_{s}+Y_{a} \alpha_{a}\right]}{\left[Y_{a}+2 Y_{s}\right]}\)
3 \(\dfrac{l_{0} \Delta T\left[Y_{s} \alpha_{s}+Y_{a} \alpha_{a}\right]}{\left[Y_{a}+Y_{s}\right]}\)
4 \(\dfrac{l_{0} \Delta T\left[2 \alpha_{s}+\alpha_{a}\right] Y_{s} Y_{a}}{\left[Y_{a}+Y_{s}\right]}\)
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PHXI11:THERMAL PROPERTIES OF MATTER

366729 A bimetallic strip is made of aluminium and steel \(\left(\alpha_{A l}>\alpha_{\text {steel }}\right)\). On heating, the strip will

1 Remain straight
2 Get twisted
3 Will bend with aluminium on concave side
4 Will bend with steel on concave side
PHXI11:THERMAL PROPERTIES OF MATTER

366730 An iron bar of length \(10\;m\) is heated from \(0^\circ C\) to \(100^\circ C\). If the coefficient of linear thermal expansion of iron is \(10 \times 10^{-6} /{ }^{\circ} \mathrm{C}\), the increase in the length of bar is

1 \(0.5\;cm\)
2 \(1.0\;cm\)
3 \(1.5\;cm\)
4 \(2.0\;cm\)
PHXI11:THERMAL PROPERTIES OF MATTER

366731 The material whose elasticity remains constant even when the temperature is changed is

1 Bimetallic strip
2 Aluminum
3 Invar steel
4 Alnico
PHXI11:THERMAL PROPERTIES OF MATTER

366732 A rail track made of steel having length \(10\;cm\) is clamped on a railway line at its two ends (figure). On a summer day due to rise in temperature by \(20^\circ C\). It is deformed as shown in figure. Find \(x\) (displacement of the centre) if \({\alpha _{{\rm{steel }}}} = 1.2 \times {10^{ - 5}}/^\circ C\)
supporting img

1 \(15\sqrt {30} \times {10^{ - 3}}\;cm\)
2 \(20\sqrt {30} \times {10^{ - 3}}\;cm\)
3 \(25\sqrt {30} \times {10^{ - 3}}\;cm\)
4 \(10\sqrt {30} \times {10^{ - 3}}\;cm\)
PHXI11:THERMAL PROPERTIES OF MATTER

366733 Two steel rods and an aluminium rod of length \(l_{0}\) and equal cross section are joined rigidly at their eand as shown in the figure below. All the rods are in a state of zero tension at \(0^\circ C\). Find the length of the system when the temperature is raised to \(\Delta T\). Coefficient of linear expansion of aluminium and steel are \(\alpha_{a}\) and \(\alpha_{s}\) respectively. Young's modulus of aluminium and steel are \(Y_{a}\) and \(Y_{s}\) respectively \(\left(\alpha_{s}>\alpha_{a}\right)\).
supporting img

1 \(l_{0} \Delta T\left[\alpha_{s}+\alpha_{a}\right]\)
2 \(\dfrac{l_{0} \Delta T\left[2 Y_{s} \alpha_{s}+Y_{a} \alpha_{a}\right]}{\left[Y_{a}+2 Y_{s}\right]}\)
3 \(\dfrac{l_{0} \Delta T\left[Y_{s} \alpha_{s}+Y_{a} \alpha_{a}\right]}{\left[Y_{a}+Y_{s}\right]}\)
4 \(\dfrac{l_{0} \Delta T\left[2 \alpha_{s}+\alpha_{a}\right] Y_{s} Y_{a}}{\left[Y_{a}+Y_{s}\right]}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366729 A bimetallic strip is made of aluminium and steel \(\left(\alpha_{A l}>\alpha_{\text {steel }}\right)\). On heating, the strip will

1 Remain straight
2 Get twisted
3 Will bend with aluminium on concave side
4 Will bend with steel on concave side
PHXI11:THERMAL PROPERTIES OF MATTER

366730 An iron bar of length \(10\;m\) is heated from \(0^\circ C\) to \(100^\circ C\). If the coefficient of linear thermal expansion of iron is \(10 \times 10^{-6} /{ }^{\circ} \mathrm{C}\), the increase in the length of bar is

1 \(0.5\;cm\)
2 \(1.0\;cm\)
3 \(1.5\;cm\)
4 \(2.0\;cm\)
PHXI11:THERMAL PROPERTIES OF MATTER

366731 The material whose elasticity remains constant even when the temperature is changed is

1 Bimetallic strip
2 Aluminum
3 Invar steel
4 Alnico
PHXI11:THERMAL PROPERTIES OF MATTER

366732 A rail track made of steel having length \(10\;cm\) is clamped on a railway line at its two ends (figure). On a summer day due to rise in temperature by \(20^\circ C\). It is deformed as shown in figure. Find \(x\) (displacement of the centre) if \({\alpha _{{\rm{steel }}}} = 1.2 \times {10^{ - 5}}/^\circ C\)
supporting img

1 \(15\sqrt {30} \times {10^{ - 3}}\;cm\)
2 \(20\sqrt {30} \times {10^{ - 3}}\;cm\)
3 \(25\sqrt {30} \times {10^{ - 3}}\;cm\)
4 \(10\sqrt {30} \times {10^{ - 3}}\;cm\)
PHXI11:THERMAL PROPERTIES OF MATTER

366733 Two steel rods and an aluminium rod of length \(l_{0}\) and equal cross section are joined rigidly at their eand as shown in the figure below. All the rods are in a state of zero tension at \(0^\circ C\). Find the length of the system when the temperature is raised to \(\Delta T\). Coefficient of linear expansion of aluminium and steel are \(\alpha_{a}\) and \(\alpha_{s}\) respectively. Young's modulus of aluminium and steel are \(Y_{a}\) and \(Y_{s}\) respectively \(\left(\alpha_{s}>\alpha_{a}\right)\).
supporting img

1 \(l_{0} \Delta T\left[\alpha_{s}+\alpha_{a}\right]\)
2 \(\dfrac{l_{0} \Delta T\left[2 Y_{s} \alpha_{s}+Y_{a} \alpha_{a}\right]}{\left[Y_{a}+2 Y_{s}\right]}\)
3 \(\dfrac{l_{0} \Delta T\left[Y_{s} \alpha_{s}+Y_{a} \alpha_{a}\right]}{\left[Y_{a}+Y_{s}\right]}\)
4 \(\dfrac{l_{0} \Delta T\left[2 \alpha_{s}+\alpha_{a}\right] Y_{s} Y_{a}}{\left[Y_{a}+Y_{s}\right]}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366729 A bimetallic strip is made of aluminium and steel \(\left(\alpha_{A l}>\alpha_{\text {steel }}\right)\). On heating, the strip will

1 Remain straight
2 Get twisted
3 Will bend with aluminium on concave side
4 Will bend with steel on concave side
PHXI11:THERMAL PROPERTIES OF MATTER

366730 An iron bar of length \(10\;m\) is heated from \(0^\circ C\) to \(100^\circ C\). If the coefficient of linear thermal expansion of iron is \(10 \times 10^{-6} /{ }^{\circ} \mathrm{C}\), the increase in the length of bar is

1 \(0.5\;cm\)
2 \(1.0\;cm\)
3 \(1.5\;cm\)
4 \(2.0\;cm\)
PHXI11:THERMAL PROPERTIES OF MATTER

366731 The material whose elasticity remains constant even when the temperature is changed is

1 Bimetallic strip
2 Aluminum
3 Invar steel
4 Alnico
PHXI11:THERMAL PROPERTIES OF MATTER

366732 A rail track made of steel having length \(10\;cm\) is clamped on a railway line at its two ends (figure). On a summer day due to rise in temperature by \(20^\circ C\). It is deformed as shown in figure. Find \(x\) (displacement of the centre) if \({\alpha _{{\rm{steel }}}} = 1.2 \times {10^{ - 5}}/^\circ C\)
supporting img

1 \(15\sqrt {30} \times {10^{ - 3}}\;cm\)
2 \(20\sqrt {30} \times {10^{ - 3}}\;cm\)
3 \(25\sqrt {30} \times {10^{ - 3}}\;cm\)
4 \(10\sqrt {30} \times {10^{ - 3}}\;cm\)
PHXI11:THERMAL PROPERTIES OF MATTER

366733 Two steel rods and an aluminium rod of length \(l_{0}\) and equal cross section are joined rigidly at their eand as shown in the figure below. All the rods are in a state of zero tension at \(0^\circ C\). Find the length of the system when the temperature is raised to \(\Delta T\). Coefficient of linear expansion of aluminium and steel are \(\alpha_{a}\) and \(\alpha_{s}\) respectively. Young's modulus of aluminium and steel are \(Y_{a}\) and \(Y_{s}\) respectively \(\left(\alpha_{s}>\alpha_{a}\right)\).
supporting img

1 \(l_{0} \Delta T\left[\alpha_{s}+\alpha_{a}\right]\)
2 \(\dfrac{l_{0} \Delta T\left[2 Y_{s} \alpha_{s}+Y_{a} \alpha_{a}\right]}{\left[Y_{a}+2 Y_{s}\right]}\)
3 \(\dfrac{l_{0} \Delta T\left[Y_{s} \alpha_{s}+Y_{a} \alpha_{a}\right]}{\left[Y_{a}+Y_{s}\right]}\)
4 \(\dfrac{l_{0} \Delta T\left[2 \alpha_{s}+\alpha_{a}\right] Y_{s} Y_{a}}{\left[Y_{a}+Y_{s}\right]}\)