Thermal Expansion
PHXI11:THERMAL PROPERTIES OF MATTER

366806 A rod is fixed between two rigid supports at \(50^\circ C\). The coefficient of linear expansion of material of \(rod\,2 \times {10^{ - 5}}/^\circ C\) and young's modulus is \(1.5 \times {10^{11}}\;N{\rm{/}}{m^2}\). What is the stress developed in the rod if temperature of rod becomes \(70^\circ C\)?

1 \(3 \times {10^4}\;N{\rm{/}}{m^2}\)
2 \(6 \times {10^7}\;N{\rm{/}}{m^2}\)
3 \(9 \times {10^{12}}\;N{\rm{/}}{m^2}\)
4 \(11 \times {10^{11}}\;N{\rm{/}}{m^2}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366807 A metal rod of length ' \(L\) ' and cross - sectional area ' \(A\) ' is heated through \(T^\circ C\). What is the force required to prevent the expansion of the rod length wise?

1 \(\dfrac{Y A \alpha T}{(1-\alpha T)}\)
2 \(\dfrac{Y A \alpha T}{(1+\alpha T)}\)
3 \(\dfrac{(1+\alpha T)}{Y A \alpha T}\)
4 \(\dfrac{(1-\alpha T)}{Y A \alpha T}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366808 A wooden wheel of radius \(R\) is made of two semicircular part (see figure). The two parts are held together by ring made of a metal strip cross sectional area \(A\) and length \(L\). \(L\) is slightly less than \(2 \pi R\). To fit the ring on the wheel, it is heated so that its temperature rises by \(\Delta T\) and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the cofficient of linear eaxpansion of the metal is \(\alpha\), and its Young's modulus is Y, the force that one part of the wheel applies on the other part is:
supporting img

1 \(2 \pi S Y \alpha \Delta T\)
2 \(S Y \alpha \Delta T\)
3 \(\pi S Y \alpha \Delta T\)
4 \(2 S Y \alpha \Delta T\)
PHXI11:THERMAL PROPERTIES OF MATTER

366809 Two uniform rods \(A B\) and \(B C\) have Young's modulus \(1.2 \times {10^{11}}\;N/{m^2}\) and \(1.5 \times {10^{11}}\;N/{m^2}\) respectively. If coefficient of linear expansion of \(AB\) is \(1.5 \times {10^{ - 5}}/^\circ C\) and both have equal area of cross section, then coefficient of linear expansion of \(BC\), for which there is no shift of the junction at all temperatures, is
supporting img

1 \(1.5 \times {10^{ - 5}}/^\circ C\)
2 \(1.2 \times {10^{ - 5}}/^\circ C\)
3 \(0.6 \times {10^{ - 5}}/^\circ C\)
4 \(0.75 \times {10^{ - 5}}/^\circ C\)
PHXI11:THERMAL PROPERTIES OF MATTER

366810 An iron bar of length \(l\) and having a cross-section \(A\) is heated from 0 to \(100^\circ C\). If this bar is so held that it is not permitted to expand or bend, the force that is developed, is

1 Independent of the length of the bar
2 Inversely proportional to the cross-sectional area of the bar
3 Directly proportional to the length of the bar
4 Inversely proportional to the length of the bar
PHXI11:THERMAL PROPERTIES OF MATTER

366806 A rod is fixed between two rigid supports at \(50^\circ C\). The coefficient of linear expansion of material of \(rod\,2 \times {10^{ - 5}}/^\circ C\) and young's modulus is \(1.5 \times {10^{11}}\;N{\rm{/}}{m^2}\). What is the stress developed in the rod if temperature of rod becomes \(70^\circ C\)?

1 \(3 \times {10^4}\;N{\rm{/}}{m^2}\)
2 \(6 \times {10^7}\;N{\rm{/}}{m^2}\)
3 \(9 \times {10^{12}}\;N{\rm{/}}{m^2}\)
4 \(11 \times {10^{11}}\;N{\rm{/}}{m^2}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366807 A metal rod of length ' \(L\) ' and cross - sectional area ' \(A\) ' is heated through \(T^\circ C\). What is the force required to prevent the expansion of the rod length wise?

1 \(\dfrac{Y A \alpha T}{(1-\alpha T)}\)
2 \(\dfrac{Y A \alpha T}{(1+\alpha T)}\)
3 \(\dfrac{(1+\alpha T)}{Y A \alpha T}\)
4 \(\dfrac{(1-\alpha T)}{Y A \alpha T}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366808 A wooden wheel of radius \(R\) is made of two semicircular part (see figure). The two parts are held together by ring made of a metal strip cross sectional area \(A\) and length \(L\). \(L\) is slightly less than \(2 \pi R\). To fit the ring on the wheel, it is heated so that its temperature rises by \(\Delta T\) and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the cofficient of linear eaxpansion of the metal is \(\alpha\), and its Young's modulus is Y, the force that one part of the wheel applies on the other part is:
supporting img

1 \(2 \pi S Y \alpha \Delta T\)
2 \(S Y \alpha \Delta T\)
3 \(\pi S Y \alpha \Delta T\)
4 \(2 S Y \alpha \Delta T\)
PHXI11:THERMAL PROPERTIES OF MATTER

366809 Two uniform rods \(A B\) and \(B C\) have Young's modulus \(1.2 \times {10^{11}}\;N/{m^2}\) and \(1.5 \times {10^{11}}\;N/{m^2}\) respectively. If coefficient of linear expansion of \(AB\) is \(1.5 \times {10^{ - 5}}/^\circ C\) and both have equal area of cross section, then coefficient of linear expansion of \(BC\), for which there is no shift of the junction at all temperatures, is
supporting img

1 \(1.5 \times {10^{ - 5}}/^\circ C\)
2 \(1.2 \times {10^{ - 5}}/^\circ C\)
3 \(0.6 \times {10^{ - 5}}/^\circ C\)
4 \(0.75 \times {10^{ - 5}}/^\circ C\)
PHXI11:THERMAL PROPERTIES OF MATTER

366810 An iron bar of length \(l\) and having a cross-section \(A\) is heated from 0 to \(100^\circ C\). If this bar is so held that it is not permitted to expand or bend, the force that is developed, is

1 Independent of the length of the bar
2 Inversely proportional to the cross-sectional area of the bar
3 Directly proportional to the length of the bar
4 Inversely proportional to the length of the bar
PHXI11:THERMAL PROPERTIES OF MATTER

366806 A rod is fixed between two rigid supports at \(50^\circ C\). The coefficient of linear expansion of material of \(rod\,2 \times {10^{ - 5}}/^\circ C\) and young's modulus is \(1.5 \times {10^{11}}\;N{\rm{/}}{m^2}\). What is the stress developed in the rod if temperature of rod becomes \(70^\circ C\)?

1 \(3 \times {10^4}\;N{\rm{/}}{m^2}\)
2 \(6 \times {10^7}\;N{\rm{/}}{m^2}\)
3 \(9 \times {10^{12}}\;N{\rm{/}}{m^2}\)
4 \(11 \times {10^{11}}\;N{\rm{/}}{m^2}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366807 A metal rod of length ' \(L\) ' and cross - sectional area ' \(A\) ' is heated through \(T^\circ C\). What is the force required to prevent the expansion of the rod length wise?

1 \(\dfrac{Y A \alpha T}{(1-\alpha T)}\)
2 \(\dfrac{Y A \alpha T}{(1+\alpha T)}\)
3 \(\dfrac{(1+\alpha T)}{Y A \alpha T}\)
4 \(\dfrac{(1-\alpha T)}{Y A \alpha T}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366808 A wooden wheel of radius \(R\) is made of two semicircular part (see figure). The two parts are held together by ring made of a metal strip cross sectional area \(A\) and length \(L\). \(L\) is slightly less than \(2 \pi R\). To fit the ring on the wheel, it is heated so that its temperature rises by \(\Delta T\) and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the cofficient of linear eaxpansion of the metal is \(\alpha\), and its Young's modulus is Y, the force that one part of the wheel applies on the other part is:
supporting img

1 \(2 \pi S Y \alpha \Delta T\)
2 \(S Y \alpha \Delta T\)
3 \(\pi S Y \alpha \Delta T\)
4 \(2 S Y \alpha \Delta T\)
PHXI11:THERMAL PROPERTIES OF MATTER

366809 Two uniform rods \(A B\) and \(B C\) have Young's modulus \(1.2 \times {10^{11}}\;N/{m^2}\) and \(1.5 \times {10^{11}}\;N/{m^2}\) respectively. If coefficient of linear expansion of \(AB\) is \(1.5 \times {10^{ - 5}}/^\circ C\) and both have equal area of cross section, then coefficient of linear expansion of \(BC\), for which there is no shift of the junction at all temperatures, is
supporting img

1 \(1.5 \times {10^{ - 5}}/^\circ C\)
2 \(1.2 \times {10^{ - 5}}/^\circ C\)
3 \(0.6 \times {10^{ - 5}}/^\circ C\)
4 \(0.75 \times {10^{ - 5}}/^\circ C\)
PHXI11:THERMAL PROPERTIES OF MATTER

366810 An iron bar of length \(l\) and having a cross-section \(A\) is heated from 0 to \(100^\circ C\). If this bar is so held that it is not permitted to expand or bend, the force that is developed, is

1 Independent of the length of the bar
2 Inversely proportional to the cross-sectional area of the bar
3 Directly proportional to the length of the bar
4 Inversely proportional to the length of the bar
PHXI11:THERMAL PROPERTIES OF MATTER

366806 A rod is fixed between two rigid supports at \(50^\circ C\). The coefficient of linear expansion of material of \(rod\,2 \times {10^{ - 5}}/^\circ C\) and young's modulus is \(1.5 \times {10^{11}}\;N{\rm{/}}{m^2}\). What is the stress developed in the rod if temperature of rod becomes \(70^\circ C\)?

1 \(3 \times {10^4}\;N{\rm{/}}{m^2}\)
2 \(6 \times {10^7}\;N{\rm{/}}{m^2}\)
3 \(9 \times {10^{12}}\;N{\rm{/}}{m^2}\)
4 \(11 \times {10^{11}}\;N{\rm{/}}{m^2}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366807 A metal rod of length ' \(L\) ' and cross - sectional area ' \(A\) ' is heated through \(T^\circ C\). What is the force required to prevent the expansion of the rod length wise?

1 \(\dfrac{Y A \alpha T}{(1-\alpha T)}\)
2 \(\dfrac{Y A \alpha T}{(1+\alpha T)}\)
3 \(\dfrac{(1+\alpha T)}{Y A \alpha T}\)
4 \(\dfrac{(1-\alpha T)}{Y A \alpha T}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366808 A wooden wheel of radius \(R\) is made of two semicircular part (see figure). The two parts are held together by ring made of a metal strip cross sectional area \(A\) and length \(L\). \(L\) is slightly less than \(2 \pi R\). To fit the ring on the wheel, it is heated so that its temperature rises by \(\Delta T\) and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the cofficient of linear eaxpansion of the metal is \(\alpha\), and its Young's modulus is Y, the force that one part of the wheel applies on the other part is:
supporting img

1 \(2 \pi S Y \alpha \Delta T\)
2 \(S Y \alpha \Delta T\)
3 \(\pi S Y \alpha \Delta T\)
4 \(2 S Y \alpha \Delta T\)
PHXI11:THERMAL PROPERTIES OF MATTER

366809 Two uniform rods \(A B\) and \(B C\) have Young's modulus \(1.2 \times {10^{11}}\;N/{m^2}\) and \(1.5 \times {10^{11}}\;N/{m^2}\) respectively. If coefficient of linear expansion of \(AB\) is \(1.5 \times {10^{ - 5}}/^\circ C\) and both have equal area of cross section, then coefficient of linear expansion of \(BC\), for which there is no shift of the junction at all temperatures, is
supporting img

1 \(1.5 \times {10^{ - 5}}/^\circ C\)
2 \(1.2 \times {10^{ - 5}}/^\circ C\)
3 \(0.6 \times {10^{ - 5}}/^\circ C\)
4 \(0.75 \times {10^{ - 5}}/^\circ C\)
PHXI11:THERMAL PROPERTIES OF MATTER

366810 An iron bar of length \(l\) and having a cross-section \(A\) is heated from 0 to \(100^\circ C\). If this bar is so held that it is not permitted to expand or bend, the force that is developed, is

1 Independent of the length of the bar
2 Inversely proportional to the cross-sectional area of the bar
3 Directly proportional to the length of the bar
4 Inversely proportional to the length of the bar
PHXI11:THERMAL PROPERTIES OF MATTER

366806 A rod is fixed between two rigid supports at \(50^\circ C\). The coefficient of linear expansion of material of \(rod\,2 \times {10^{ - 5}}/^\circ C\) and young's modulus is \(1.5 \times {10^{11}}\;N{\rm{/}}{m^2}\). What is the stress developed in the rod if temperature of rod becomes \(70^\circ C\)?

1 \(3 \times {10^4}\;N{\rm{/}}{m^2}\)
2 \(6 \times {10^7}\;N{\rm{/}}{m^2}\)
3 \(9 \times {10^{12}}\;N{\rm{/}}{m^2}\)
4 \(11 \times {10^{11}}\;N{\rm{/}}{m^2}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366807 A metal rod of length ' \(L\) ' and cross - sectional area ' \(A\) ' is heated through \(T^\circ C\). What is the force required to prevent the expansion of the rod length wise?

1 \(\dfrac{Y A \alpha T}{(1-\alpha T)}\)
2 \(\dfrac{Y A \alpha T}{(1+\alpha T)}\)
3 \(\dfrac{(1+\alpha T)}{Y A \alpha T}\)
4 \(\dfrac{(1-\alpha T)}{Y A \alpha T}\)
PHXI11:THERMAL PROPERTIES OF MATTER

366808 A wooden wheel of radius \(R\) is made of two semicircular part (see figure). The two parts are held together by ring made of a metal strip cross sectional area \(A\) and length \(L\). \(L\) is slightly less than \(2 \pi R\). To fit the ring on the wheel, it is heated so that its temperature rises by \(\Delta T\) and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the cofficient of linear eaxpansion of the metal is \(\alpha\), and its Young's modulus is Y, the force that one part of the wheel applies on the other part is:
supporting img

1 \(2 \pi S Y \alpha \Delta T\)
2 \(S Y \alpha \Delta T\)
3 \(\pi S Y \alpha \Delta T\)
4 \(2 S Y \alpha \Delta T\)
PHXI11:THERMAL PROPERTIES OF MATTER

366809 Two uniform rods \(A B\) and \(B C\) have Young's modulus \(1.2 \times {10^{11}}\;N/{m^2}\) and \(1.5 \times {10^{11}}\;N/{m^2}\) respectively. If coefficient of linear expansion of \(AB\) is \(1.5 \times {10^{ - 5}}/^\circ C\) and both have equal area of cross section, then coefficient of linear expansion of \(BC\), for which there is no shift of the junction at all temperatures, is
supporting img

1 \(1.5 \times {10^{ - 5}}/^\circ C\)
2 \(1.2 \times {10^{ - 5}}/^\circ C\)
3 \(0.6 \times {10^{ - 5}}/^\circ C\)
4 \(0.75 \times {10^{ - 5}}/^\circ C\)
PHXI11:THERMAL PROPERTIES OF MATTER

366810 An iron bar of length \(l\) and having a cross-section \(A\) is heated from 0 to \(100^\circ C\). If this bar is so held that it is not permitted to expand or bend, the force that is developed, is

1 Independent of the length of the bar
2 Inversely proportional to the cross-sectional area of the bar
3 Directly proportional to the length of the bar
4 Inversely proportional to the length of the bar