Elastic Moduli
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369818 The Young's modulus of brass and steel are respectively \(1.0 \times {10^{11}}N{m^{ - 2}}\) and \(2.0 \times {10^{11}}N{m^{ - 2}}.\) A brass wire and a steel wire of the same length are extended by \(1\;mm\) each under the same force. If radii of brass and steel wires are \(R_{B}\) and \(R_{S}\) respectively, then

1 \(R_{S}=\sqrt{2} R_{B}\)
2 \(R_{S}=\dfrac{R_{B}}{\sqrt{2}}\)
3 \(R_{S}=4 R_{B}\)
4 \(R_{S}=\dfrac{R_{B}}{2}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369819 A metal wire of length \(L_{1}\) and area of cross section A is attached to a rigid support. Another metal wire of length \(L_{2}\) and of the same cross sectional area is attached to the free end of the first wire. A body of mass \(M\) is then suspended from the free end of the second wire. If \(Y_{1}\) and \(Y_{2}\) are the Young's moduli of the wires respectively, the effective force constant of the system of two wires is

1 \(\left[\left(Y_{1} Y_{2}\right) A\right] /\left[\left(L_{1} L_{2}\right)\right]^{1 / 2}\)
2 \(\left[\left(Y_{1} Y_{2}\right) A\right] /\left[2\left(Y_{1} L_{2}+Y_{2} L_{1}\right)\right]\)
3 \(\left(Y_{1} Y_{2}\right)^{1 / 2} A /\left(L_{1} L_{2}\right)^{1 / 2}\)
4 \(\left[\left(Y_{1} Y_{2}\right) A\right] /\left(Y_{1} L_{2}+Y_{2} L_{1}\right)\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369820 The diameter of a brass rod is \(4\,mm\) and Young's modulus of brass is \(9 \times {10^{10}}\;N{\rm{/}}{m^2}\). The force required to stretch by \(0.1 \%\) of its length is:

1 \(36\,N\)
2 \(360\,\pi N\)
3 \(144\pi \times {10^3}\,N\)
4 \(36\pi \times {10^5}\,N\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369821 'Young's modulus' is defined as the ratio of

1 Bulk stress and longitudinal strain
2 Hydraulic stress and hydraulic strain
3 Shearing stress and shearing strain
4 Tensile stress and longitudinal strain
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369822 Two identical wires of substances ' \(\mathrm{P}\) ' and ' \(\mathrm{Q}\) ' are subjected to equal stretching force along the length. If the elongation of ' \(Q\) ' is more than that of ' \(\mathrm{P}\) ', then

1 Both P and Q are equally elastic
2 \(P\) is more elastic than \(Q\)
3 \(P\) is plastic and \(Q\) is elastic
4 \(Q\) is more elastic than \(P\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369818 The Young's modulus of brass and steel are respectively \(1.0 \times {10^{11}}N{m^{ - 2}}\) and \(2.0 \times {10^{11}}N{m^{ - 2}}.\) A brass wire and a steel wire of the same length are extended by \(1\;mm\) each under the same force. If radii of brass and steel wires are \(R_{B}\) and \(R_{S}\) respectively, then

1 \(R_{S}=\sqrt{2} R_{B}\)
2 \(R_{S}=\dfrac{R_{B}}{\sqrt{2}}\)
3 \(R_{S}=4 R_{B}\)
4 \(R_{S}=\dfrac{R_{B}}{2}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369819 A metal wire of length \(L_{1}\) and area of cross section A is attached to a rigid support. Another metal wire of length \(L_{2}\) and of the same cross sectional area is attached to the free end of the first wire. A body of mass \(M\) is then suspended from the free end of the second wire. If \(Y_{1}\) and \(Y_{2}\) are the Young's moduli of the wires respectively, the effective force constant of the system of two wires is

1 \(\left[\left(Y_{1} Y_{2}\right) A\right] /\left[\left(L_{1} L_{2}\right)\right]^{1 / 2}\)
2 \(\left[\left(Y_{1} Y_{2}\right) A\right] /\left[2\left(Y_{1} L_{2}+Y_{2} L_{1}\right)\right]\)
3 \(\left(Y_{1} Y_{2}\right)^{1 / 2} A /\left(L_{1} L_{2}\right)^{1 / 2}\)
4 \(\left[\left(Y_{1} Y_{2}\right) A\right] /\left(Y_{1} L_{2}+Y_{2} L_{1}\right)\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369820 The diameter of a brass rod is \(4\,mm\) and Young's modulus of brass is \(9 \times {10^{10}}\;N{\rm{/}}{m^2}\). The force required to stretch by \(0.1 \%\) of its length is:

1 \(36\,N\)
2 \(360\,\pi N\)
3 \(144\pi \times {10^3}\,N\)
4 \(36\pi \times {10^5}\,N\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369821 'Young's modulus' is defined as the ratio of

1 Bulk stress and longitudinal strain
2 Hydraulic stress and hydraulic strain
3 Shearing stress and shearing strain
4 Tensile stress and longitudinal strain
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369822 Two identical wires of substances ' \(\mathrm{P}\) ' and ' \(\mathrm{Q}\) ' are subjected to equal stretching force along the length. If the elongation of ' \(Q\) ' is more than that of ' \(\mathrm{P}\) ', then

1 Both P and Q are equally elastic
2 \(P\) is more elastic than \(Q\)
3 \(P\) is plastic and \(Q\) is elastic
4 \(Q\) is more elastic than \(P\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369818 The Young's modulus of brass and steel are respectively \(1.0 \times {10^{11}}N{m^{ - 2}}\) and \(2.0 \times {10^{11}}N{m^{ - 2}}.\) A brass wire and a steel wire of the same length are extended by \(1\;mm\) each under the same force. If radii of brass and steel wires are \(R_{B}\) and \(R_{S}\) respectively, then

1 \(R_{S}=\sqrt{2} R_{B}\)
2 \(R_{S}=\dfrac{R_{B}}{\sqrt{2}}\)
3 \(R_{S}=4 R_{B}\)
4 \(R_{S}=\dfrac{R_{B}}{2}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369819 A metal wire of length \(L_{1}\) and area of cross section A is attached to a rigid support. Another metal wire of length \(L_{2}\) and of the same cross sectional area is attached to the free end of the first wire. A body of mass \(M\) is then suspended from the free end of the second wire. If \(Y_{1}\) and \(Y_{2}\) are the Young's moduli of the wires respectively, the effective force constant of the system of two wires is

1 \(\left[\left(Y_{1} Y_{2}\right) A\right] /\left[\left(L_{1} L_{2}\right)\right]^{1 / 2}\)
2 \(\left[\left(Y_{1} Y_{2}\right) A\right] /\left[2\left(Y_{1} L_{2}+Y_{2} L_{1}\right)\right]\)
3 \(\left(Y_{1} Y_{2}\right)^{1 / 2} A /\left(L_{1} L_{2}\right)^{1 / 2}\)
4 \(\left[\left(Y_{1} Y_{2}\right) A\right] /\left(Y_{1} L_{2}+Y_{2} L_{1}\right)\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369820 The diameter of a brass rod is \(4\,mm\) and Young's modulus of brass is \(9 \times {10^{10}}\;N{\rm{/}}{m^2}\). The force required to stretch by \(0.1 \%\) of its length is:

1 \(36\,N\)
2 \(360\,\pi N\)
3 \(144\pi \times {10^3}\,N\)
4 \(36\pi \times {10^5}\,N\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369821 'Young's modulus' is defined as the ratio of

1 Bulk stress and longitudinal strain
2 Hydraulic stress and hydraulic strain
3 Shearing stress and shearing strain
4 Tensile stress and longitudinal strain
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369822 Two identical wires of substances ' \(\mathrm{P}\) ' and ' \(\mathrm{Q}\) ' are subjected to equal stretching force along the length. If the elongation of ' \(Q\) ' is more than that of ' \(\mathrm{P}\) ', then

1 Both P and Q are equally elastic
2 \(P\) is more elastic than \(Q\)
3 \(P\) is plastic and \(Q\) is elastic
4 \(Q\) is more elastic than \(P\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369818 The Young's modulus of brass and steel are respectively \(1.0 \times {10^{11}}N{m^{ - 2}}\) and \(2.0 \times {10^{11}}N{m^{ - 2}}.\) A brass wire and a steel wire of the same length are extended by \(1\;mm\) each under the same force. If radii of brass and steel wires are \(R_{B}\) and \(R_{S}\) respectively, then

1 \(R_{S}=\sqrt{2} R_{B}\)
2 \(R_{S}=\dfrac{R_{B}}{\sqrt{2}}\)
3 \(R_{S}=4 R_{B}\)
4 \(R_{S}=\dfrac{R_{B}}{2}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369819 A metal wire of length \(L_{1}\) and area of cross section A is attached to a rigid support. Another metal wire of length \(L_{2}\) and of the same cross sectional area is attached to the free end of the first wire. A body of mass \(M\) is then suspended from the free end of the second wire. If \(Y_{1}\) and \(Y_{2}\) are the Young's moduli of the wires respectively, the effective force constant of the system of two wires is

1 \(\left[\left(Y_{1} Y_{2}\right) A\right] /\left[\left(L_{1} L_{2}\right)\right]^{1 / 2}\)
2 \(\left[\left(Y_{1} Y_{2}\right) A\right] /\left[2\left(Y_{1} L_{2}+Y_{2} L_{1}\right)\right]\)
3 \(\left(Y_{1} Y_{2}\right)^{1 / 2} A /\left(L_{1} L_{2}\right)^{1 / 2}\)
4 \(\left[\left(Y_{1} Y_{2}\right) A\right] /\left(Y_{1} L_{2}+Y_{2} L_{1}\right)\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369820 The diameter of a brass rod is \(4\,mm\) and Young's modulus of brass is \(9 \times {10^{10}}\;N{\rm{/}}{m^2}\). The force required to stretch by \(0.1 \%\) of its length is:

1 \(36\,N\)
2 \(360\,\pi N\)
3 \(144\pi \times {10^3}\,N\)
4 \(36\pi \times {10^5}\,N\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369821 'Young's modulus' is defined as the ratio of

1 Bulk stress and longitudinal strain
2 Hydraulic stress and hydraulic strain
3 Shearing stress and shearing strain
4 Tensile stress and longitudinal strain
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369822 Two identical wires of substances ' \(\mathrm{P}\) ' and ' \(\mathrm{Q}\) ' are subjected to equal stretching force along the length. If the elongation of ' \(Q\) ' is more than that of ' \(\mathrm{P}\) ', then

1 Both P and Q are equally elastic
2 \(P\) is more elastic than \(Q\)
3 \(P\) is plastic and \(Q\) is elastic
4 \(Q\) is more elastic than \(P\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369818 The Young's modulus of brass and steel are respectively \(1.0 \times {10^{11}}N{m^{ - 2}}\) and \(2.0 \times {10^{11}}N{m^{ - 2}}.\) A brass wire and a steel wire of the same length are extended by \(1\;mm\) each under the same force. If radii of brass and steel wires are \(R_{B}\) and \(R_{S}\) respectively, then

1 \(R_{S}=\sqrt{2} R_{B}\)
2 \(R_{S}=\dfrac{R_{B}}{\sqrt{2}}\)
3 \(R_{S}=4 R_{B}\)
4 \(R_{S}=\dfrac{R_{B}}{2}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369819 A metal wire of length \(L_{1}\) and area of cross section A is attached to a rigid support. Another metal wire of length \(L_{2}\) and of the same cross sectional area is attached to the free end of the first wire. A body of mass \(M\) is then suspended from the free end of the second wire. If \(Y_{1}\) and \(Y_{2}\) are the Young's moduli of the wires respectively, the effective force constant of the system of two wires is

1 \(\left[\left(Y_{1} Y_{2}\right) A\right] /\left[\left(L_{1} L_{2}\right)\right]^{1 / 2}\)
2 \(\left[\left(Y_{1} Y_{2}\right) A\right] /\left[2\left(Y_{1} L_{2}+Y_{2} L_{1}\right)\right]\)
3 \(\left(Y_{1} Y_{2}\right)^{1 / 2} A /\left(L_{1} L_{2}\right)^{1 / 2}\)
4 \(\left[\left(Y_{1} Y_{2}\right) A\right] /\left(Y_{1} L_{2}+Y_{2} L_{1}\right)\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369820 The diameter of a brass rod is \(4\,mm\) and Young's modulus of brass is \(9 \times {10^{10}}\;N{\rm{/}}{m^2}\). The force required to stretch by \(0.1 \%\) of its length is:

1 \(36\,N\)
2 \(360\,\pi N\)
3 \(144\pi \times {10^3}\,N\)
4 \(36\pi \times {10^5}\,N\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369821 'Young's modulus' is defined as the ratio of

1 Bulk stress and longitudinal strain
2 Hydraulic stress and hydraulic strain
3 Shearing stress and shearing strain
4 Tensile stress and longitudinal strain
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369822 Two identical wires of substances ' \(\mathrm{P}\) ' and ' \(\mathrm{Q}\) ' are subjected to equal stretching force along the length. If the elongation of ' \(Q\) ' is more than that of ' \(\mathrm{P}\) ', then

1 Both P and Q are equally elastic
2 \(P\) is more elastic than \(Q\)
3 \(P\) is plastic and \(Q\) is elastic
4 \(Q\) is more elastic than \(P\)