Elastic Moduli
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369780 A wire of length \(L\) is hanging from a fixed support. The length changes from \(L_{1}\) to \(L_{2}\) when masses \(M_{1}\) and \(M_{2}\) are suspended respectively from its free end. Then \(L\) is equal to

1 \(\sqrt{L_{1} L_{2}}\)
2 \(\dfrac{L_{1}+L_{2}}{2}\)
3 \(\dfrac{L_{1} M_{2}+L_{2} M_{1}}{M_{1}+M_{2}}\)
4 \(\dfrac{L_{1} M_{2}-L_{2} M_{1}}{M_{2}-M_{1}}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369781 A rigid bar of mass \(M\) is supported symmetrically by three wires each of length \(l\). Those at each end are of copper and the middle one is of iron. The ratio of their diameter, if each is to have the same tension, is equal to

1 \(\gamma_{\text {copper }} / \gamma_{\text {iron }}\)
2 \(\sqrt{\dfrac{\gamma_{\text {iron }}}{\gamma_{\text {copper }}}}\)
3 \(\dfrac{\gamma_{\text {iron }}^{2}}{\gamma_{\text {copper }}^{2}}\)
4 \(\dfrac{\gamma_{\text {iron }}}{\gamma_{\text {copper }}}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369782 Two wires are made of the same material and have the same volume. The first wire has crosssectional area A and the second wire has crosssectional area \(3A\). If the length of the first wire is increased by \(l\) on applying a force \(F\), how much force is needed to stretch the second wire by the same amount ?

1 \(4\;F\)
2 \(F\)
3 \(6\;F\)
4 \(9\;F\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369783 A force is applied to a steel wire '\(A\)', rigidly clamped at one end. As a result elongation in the wire is \(0.2\;mm\). If same force is applied to another steel wire '\(B\)' of double the length and a diameter 2.4 times that of the wire '\(A\)', the elongation in the wire '\(B\)' will be (wires having uniform circular cross sections)

1 \(2.77 \times {10^{ - 2}}\;mm\)
2 \(6.9 \times {10^{ - 2}}\;mm\)
3 \(6.06 \times {10^{ - 2}}\;mm\)
4 \(3.0 \times {10^{ - 2}}\;mm\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369780 A wire of length \(L\) is hanging from a fixed support. The length changes from \(L_{1}\) to \(L_{2}\) when masses \(M_{1}\) and \(M_{2}\) are suspended respectively from its free end. Then \(L\) is equal to

1 \(\sqrt{L_{1} L_{2}}\)
2 \(\dfrac{L_{1}+L_{2}}{2}\)
3 \(\dfrac{L_{1} M_{2}+L_{2} M_{1}}{M_{1}+M_{2}}\)
4 \(\dfrac{L_{1} M_{2}-L_{2} M_{1}}{M_{2}-M_{1}}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369781 A rigid bar of mass \(M\) is supported symmetrically by three wires each of length \(l\). Those at each end are of copper and the middle one is of iron. The ratio of their diameter, if each is to have the same tension, is equal to

1 \(\gamma_{\text {copper }} / \gamma_{\text {iron }}\)
2 \(\sqrt{\dfrac{\gamma_{\text {iron }}}{\gamma_{\text {copper }}}}\)
3 \(\dfrac{\gamma_{\text {iron }}^{2}}{\gamma_{\text {copper }}^{2}}\)
4 \(\dfrac{\gamma_{\text {iron }}}{\gamma_{\text {copper }}}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369782 Two wires are made of the same material and have the same volume. The first wire has crosssectional area A and the second wire has crosssectional area \(3A\). If the length of the first wire is increased by \(l\) on applying a force \(F\), how much force is needed to stretch the second wire by the same amount ?

1 \(4\;F\)
2 \(F\)
3 \(6\;F\)
4 \(9\;F\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369783 A force is applied to a steel wire '\(A\)', rigidly clamped at one end. As a result elongation in the wire is \(0.2\;mm\). If same force is applied to another steel wire '\(B\)' of double the length and a diameter 2.4 times that of the wire '\(A\)', the elongation in the wire '\(B\)' will be (wires having uniform circular cross sections)

1 \(2.77 \times {10^{ - 2}}\;mm\)
2 \(6.9 \times {10^{ - 2}}\;mm\)
3 \(6.06 \times {10^{ - 2}}\;mm\)
4 \(3.0 \times {10^{ - 2}}\;mm\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369780 A wire of length \(L\) is hanging from a fixed support. The length changes from \(L_{1}\) to \(L_{2}\) when masses \(M_{1}\) and \(M_{2}\) are suspended respectively from its free end. Then \(L\) is equal to

1 \(\sqrt{L_{1} L_{2}}\)
2 \(\dfrac{L_{1}+L_{2}}{2}\)
3 \(\dfrac{L_{1} M_{2}+L_{2} M_{1}}{M_{1}+M_{2}}\)
4 \(\dfrac{L_{1} M_{2}-L_{2} M_{1}}{M_{2}-M_{1}}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369781 A rigid bar of mass \(M\) is supported symmetrically by three wires each of length \(l\). Those at each end are of copper and the middle one is of iron. The ratio of their diameter, if each is to have the same tension, is equal to

1 \(\gamma_{\text {copper }} / \gamma_{\text {iron }}\)
2 \(\sqrt{\dfrac{\gamma_{\text {iron }}}{\gamma_{\text {copper }}}}\)
3 \(\dfrac{\gamma_{\text {iron }}^{2}}{\gamma_{\text {copper }}^{2}}\)
4 \(\dfrac{\gamma_{\text {iron }}}{\gamma_{\text {copper }}}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369782 Two wires are made of the same material and have the same volume. The first wire has crosssectional area A and the second wire has crosssectional area \(3A\). If the length of the first wire is increased by \(l\) on applying a force \(F\), how much force is needed to stretch the second wire by the same amount ?

1 \(4\;F\)
2 \(F\)
3 \(6\;F\)
4 \(9\;F\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369783 A force is applied to a steel wire '\(A\)', rigidly clamped at one end. As a result elongation in the wire is \(0.2\;mm\). If same force is applied to another steel wire '\(B\)' of double the length and a diameter 2.4 times that of the wire '\(A\)', the elongation in the wire '\(B\)' will be (wires having uniform circular cross sections)

1 \(2.77 \times {10^{ - 2}}\;mm\)
2 \(6.9 \times {10^{ - 2}}\;mm\)
3 \(6.06 \times {10^{ - 2}}\;mm\)
4 \(3.0 \times {10^{ - 2}}\;mm\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369780 A wire of length \(L\) is hanging from a fixed support. The length changes from \(L_{1}\) to \(L_{2}\) when masses \(M_{1}\) and \(M_{2}\) are suspended respectively from its free end. Then \(L\) is equal to

1 \(\sqrt{L_{1} L_{2}}\)
2 \(\dfrac{L_{1}+L_{2}}{2}\)
3 \(\dfrac{L_{1} M_{2}+L_{2} M_{1}}{M_{1}+M_{2}}\)
4 \(\dfrac{L_{1} M_{2}-L_{2} M_{1}}{M_{2}-M_{1}}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369781 A rigid bar of mass \(M\) is supported symmetrically by three wires each of length \(l\). Those at each end are of copper and the middle one is of iron. The ratio of their diameter, if each is to have the same tension, is equal to

1 \(\gamma_{\text {copper }} / \gamma_{\text {iron }}\)
2 \(\sqrt{\dfrac{\gamma_{\text {iron }}}{\gamma_{\text {copper }}}}\)
3 \(\dfrac{\gamma_{\text {iron }}^{2}}{\gamma_{\text {copper }}^{2}}\)
4 \(\dfrac{\gamma_{\text {iron }}}{\gamma_{\text {copper }}}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369782 Two wires are made of the same material and have the same volume. The first wire has crosssectional area A and the second wire has crosssectional area \(3A\). If the length of the first wire is increased by \(l\) on applying a force \(F\), how much force is needed to stretch the second wire by the same amount ?

1 \(4\;F\)
2 \(F\)
3 \(6\;F\)
4 \(9\;F\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369783 A force is applied to a steel wire '\(A\)', rigidly clamped at one end. As a result elongation in the wire is \(0.2\;mm\). If same force is applied to another steel wire '\(B\)' of double the length and a diameter 2.4 times that of the wire '\(A\)', the elongation in the wire '\(B\)' will be (wires having uniform circular cross sections)

1 \(2.77 \times {10^{ - 2}}\;mm\)
2 \(6.9 \times {10^{ - 2}}\;mm\)
3 \(6.06 \times {10^{ - 2}}\;mm\)
4 \(3.0 \times {10^{ - 2}}\;mm\)