Elastic Moduli
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369823 A uniform elastic rod of cross-section area \(A\), natural length \(L\) and Young's modulus \(Y\) is placed on a smooth horizontal surface. Now two horizontal forces (of magnitude \(F\,{\text{and}}\,3\;F\) ) directed along the length of rod and in opposite direction act at two of its ends as shown. After the rod has acquired steady state, the extension of the rod will be
supporting img

1 \(\dfrac{4 F}{Y A} L\)
2 \(\dfrac{2 F}{Y A} L\)
3 \(\dfrac{3 F}{2 Y A} L\)
4 \(\dfrac{F}{Y A} L\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369824 The length of an elastic string is \(a\) metre when the longitudinal tension is \(4\;N\) and \(b\) metre when the longitudinal tension is \(5\;N\). the length of the string in meter when the longitudinal tension is \(9\;N\) is

1 \(5 b-4 a\)
2 \(a-b\)
3 \(4 a-3 b\)
4 \(2 b-\dfrac{1}{4} a\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369825 A wire of length \(L\), area of cross section \(A\) is hanging form a fixed support. The length of the wire changes to \(L_{1}\) When mass \(M\) is suspended form its free end. The expression for Young's modulus is:

1 \(\left(M g\left(L_{1} L\right)\right) / A L\)
2 \(M g L /\left(A L_{1}\right)\)
3 \(M g L / A\left(L_{1} L\right)\)
4 \(M g L_{1} / A L\) )
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369826 A metal bar of length \(L\) and area of cross section A is clamped between two rigid supports. For the material of the rod, its Young's modulus is Y and coefficient of linear expansion is \(\alpha\). If the the temperature of the rod increased by \(\Delta t^\circ {\text{ }}C\), the force exerted by the rod on the supports is

1 \(YA\,\alpha \,\Delta t\)
2 \(Y A L \Delta t\)
3 \(Y \propto AL\,\Delta t\)
4 \(\dfrac{Y L \alpha \Delta t}{A}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369823 A uniform elastic rod of cross-section area \(A\), natural length \(L\) and Young's modulus \(Y\) is placed on a smooth horizontal surface. Now two horizontal forces (of magnitude \(F\,{\text{and}}\,3\;F\) ) directed along the length of rod and in opposite direction act at two of its ends as shown. After the rod has acquired steady state, the extension of the rod will be
supporting img

1 \(\dfrac{4 F}{Y A} L\)
2 \(\dfrac{2 F}{Y A} L\)
3 \(\dfrac{3 F}{2 Y A} L\)
4 \(\dfrac{F}{Y A} L\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369824 The length of an elastic string is \(a\) metre when the longitudinal tension is \(4\;N\) and \(b\) metre when the longitudinal tension is \(5\;N\). the length of the string in meter when the longitudinal tension is \(9\;N\) is

1 \(5 b-4 a\)
2 \(a-b\)
3 \(4 a-3 b\)
4 \(2 b-\dfrac{1}{4} a\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369825 A wire of length \(L\), area of cross section \(A\) is hanging form a fixed support. The length of the wire changes to \(L_{1}\) When mass \(M\) is suspended form its free end. The expression for Young's modulus is:

1 \(\left(M g\left(L_{1} L\right)\right) / A L\)
2 \(M g L /\left(A L_{1}\right)\)
3 \(M g L / A\left(L_{1} L\right)\)
4 \(M g L_{1} / A L\) )
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369826 A metal bar of length \(L\) and area of cross section A is clamped between two rigid supports. For the material of the rod, its Young's modulus is Y and coefficient of linear expansion is \(\alpha\). If the the temperature of the rod increased by \(\Delta t^\circ {\text{ }}C\), the force exerted by the rod on the supports is

1 \(YA\,\alpha \,\Delta t\)
2 \(Y A L \Delta t\)
3 \(Y \propto AL\,\Delta t\)
4 \(\dfrac{Y L \alpha \Delta t}{A}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369823 A uniform elastic rod of cross-section area \(A\), natural length \(L\) and Young's modulus \(Y\) is placed on a smooth horizontal surface. Now two horizontal forces (of magnitude \(F\,{\text{and}}\,3\;F\) ) directed along the length of rod and in opposite direction act at two of its ends as shown. After the rod has acquired steady state, the extension of the rod will be
supporting img

1 \(\dfrac{4 F}{Y A} L\)
2 \(\dfrac{2 F}{Y A} L\)
3 \(\dfrac{3 F}{2 Y A} L\)
4 \(\dfrac{F}{Y A} L\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369824 The length of an elastic string is \(a\) metre when the longitudinal tension is \(4\;N\) and \(b\) metre when the longitudinal tension is \(5\;N\). the length of the string in meter when the longitudinal tension is \(9\;N\) is

1 \(5 b-4 a\)
2 \(a-b\)
3 \(4 a-3 b\)
4 \(2 b-\dfrac{1}{4} a\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369825 A wire of length \(L\), area of cross section \(A\) is hanging form a fixed support. The length of the wire changes to \(L_{1}\) When mass \(M\) is suspended form its free end. The expression for Young's modulus is:

1 \(\left(M g\left(L_{1} L\right)\right) / A L\)
2 \(M g L /\left(A L_{1}\right)\)
3 \(M g L / A\left(L_{1} L\right)\)
4 \(M g L_{1} / A L\) )
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369826 A metal bar of length \(L\) and area of cross section A is clamped between two rigid supports. For the material of the rod, its Young's modulus is Y and coefficient of linear expansion is \(\alpha\). If the the temperature of the rod increased by \(\Delta t^\circ {\text{ }}C\), the force exerted by the rod on the supports is

1 \(YA\,\alpha \,\Delta t\)
2 \(Y A L \Delta t\)
3 \(Y \propto AL\,\Delta t\)
4 \(\dfrac{Y L \alpha \Delta t}{A}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369823 A uniform elastic rod of cross-section area \(A\), natural length \(L\) and Young's modulus \(Y\) is placed on a smooth horizontal surface. Now two horizontal forces (of magnitude \(F\,{\text{and}}\,3\;F\) ) directed along the length of rod and in opposite direction act at two of its ends as shown. After the rod has acquired steady state, the extension of the rod will be
supporting img

1 \(\dfrac{4 F}{Y A} L\)
2 \(\dfrac{2 F}{Y A} L\)
3 \(\dfrac{3 F}{2 Y A} L\)
4 \(\dfrac{F}{Y A} L\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369824 The length of an elastic string is \(a\) metre when the longitudinal tension is \(4\;N\) and \(b\) metre when the longitudinal tension is \(5\;N\). the length of the string in meter when the longitudinal tension is \(9\;N\) is

1 \(5 b-4 a\)
2 \(a-b\)
3 \(4 a-3 b\)
4 \(2 b-\dfrac{1}{4} a\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369825 A wire of length \(L\), area of cross section \(A\) is hanging form a fixed support. The length of the wire changes to \(L_{1}\) When mass \(M\) is suspended form its free end. The expression for Young's modulus is:

1 \(\left(M g\left(L_{1} L\right)\right) / A L\)
2 \(M g L /\left(A L_{1}\right)\)
3 \(M g L / A\left(L_{1} L\right)\)
4 \(M g L_{1} / A L\) )
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369826 A metal bar of length \(L\) and area of cross section A is clamped between two rigid supports. For the material of the rod, its Young's modulus is Y and coefficient of linear expansion is \(\alpha\). If the the temperature of the rod increased by \(\Delta t^\circ {\text{ }}C\), the force exerted by the rod on the supports is

1 \(YA\,\alpha \,\Delta t\)
2 \(Y A L \Delta t\)
3 \(Y \propto AL\,\Delta t\)
4 \(\dfrac{Y L \alpha \Delta t}{A}\)