Elastic Moduli
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369728 For a given material, the Young's modulus is 2.4 times that of rigidity modulus, then Poisson's ratio is

1 \(0.2{\rm{ }}\)
2 \(0.4{\rm{ }}\)
3 \(1.2{\rm{ }}\)
4 \(2.4\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369729 The relationship between Young's modulus \(Y\), bulk modulus \(B\) and modulus of rigidity \(\eta\) is

1 \(Y=\dfrac{9 \eta B}{\eta+3 B}\)
2 \(\eta=\dfrac{9 Y B}{Y+3 B}\)
3 \(Y=\dfrac{9 \eta B}{3 \eta+B}\)
4 \(Y=\dfrac{3 \eta B}{9 \eta+B}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369730 Two wires of equal lengths and cross-section areas are suspended, as shown in the figure. If their respective Young's moduli are \({Y_{1}}\) and \({Y_{2}}\), then the equivalent Young's modulus will be
supporting img

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

369731 Identify the incorrect statement.

1 Bulk modulus is relevant for solids, liquids and gases
2 Young's modulus and shear modulus are relevant only for solids.
3 Shear modulus for liquids is infinity
4 Metals have large values of Young's modulus than elastomers
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369732 A light rod of length 2 \(m\) is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of steel and is of cross-section \(10^{-3} {~m}^{2}\) and the other is of brass of cross-section \(2 \times 10^{-3} {~m}^{2}\). Find out the distance along the rod from steel wire, at which a weight may be hung to produce equal strains in both wires. Young's modulus for brass \( = {10^{11}}N{m^{ - 2}}\) and Young's modulus for steel \(=2 \times 10^{11} {~N} {~m}^{-2}\).
supporting img

1 \(1\,m\)
2 \(3\,m\)
3 \(7\,m\)
4 \(9\,m\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369728 For a given material, the Young's modulus is 2.4 times that of rigidity modulus, then Poisson's ratio is

1 \(0.2{\rm{ }}\)
2 \(0.4{\rm{ }}\)
3 \(1.2{\rm{ }}\)
4 \(2.4\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369729 The relationship between Young's modulus \(Y\), bulk modulus \(B\) and modulus of rigidity \(\eta\) is

1 \(Y=\dfrac{9 \eta B}{\eta+3 B}\)
2 \(\eta=\dfrac{9 Y B}{Y+3 B}\)
3 \(Y=\dfrac{9 \eta B}{3 \eta+B}\)
4 \(Y=\dfrac{3 \eta B}{9 \eta+B}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369730 Two wires of equal lengths and cross-section areas are suspended, as shown in the figure. If their respective Young's moduli are \({Y_{1}}\) and \({Y_{2}}\), then the equivalent Young's modulus will be
supporting img

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

369731 Identify the incorrect statement.

1 Bulk modulus is relevant for solids, liquids and gases
2 Young's modulus and shear modulus are relevant only for solids.
3 Shear modulus for liquids is infinity
4 Metals have large values of Young's modulus than elastomers
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369732 A light rod of length 2 \(m\) is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of steel and is of cross-section \(10^{-3} {~m}^{2}\) and the other is of brass of cross-section \(2 \times 10^{-3} {~m}^{2}\). Find out the distance along the rod from steel wire, at which a weight may be hung to produce equal strains in both wires. Young's modulus for brass \( = {10^{11}}N{m^{ - 2}}\) and Young's modulus for steel \(=2 \times 10^{11} {~N} {~m}^{-2}\).
supporting img

1 \(1\,m\)
2 \(3\,m\)
3 \(7\,m\)
4 \(9\,m\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369728 For a given material, the Young's modulus is 2.4 times that of rigidity modulus, then Poisson's ratio is

1 \(0.2{\rm{ }}\)
2 \(0.4{\rm{ }}\)
3 \(1.2{\rm{ }}\)
4 \(2.4\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369729 The relationship between Young's modulus \(Y\), bulk modulus \(B\) and modulus of rigidity \(\eta\) is

1 \(Y=\dfrac{9 \eta B}{\eta+3 B}\)
2 \(\eta=\dfrac{9 Y B}{Y+3 B}\)
3 \(Y=\dfrac{9 \eta B}{3 \eta+B}\)
4 \(Y=\dfrac{3 \eta B}{9 \eta+B}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369730 Two wires of equal lengths and cross-section areas are suspended, as shown in the figure. If their respective Young's moduli are \({Y_{1}}\) and \({Y_{2}}\), then the equivalent Young's modulus will be
supporting img

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

369731 Identify the incorrect statement.

1 Bulk modulus is relevant for solids, liquids and gases
2 Young's modulus and shear modulus are relevant only for solids.
3 Shear modulus for liquids is infinity
4 Metals have large values of Young's modulus than elastomers
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369732 A light rod of length 2 \(m\) is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of steel and is of cross-section \(10^{-3} {~m}^{2}\) and the other is of brass of cross-section \(2 \times 10^{-3} {~m}^{2}\). Find out the distance along the rod from steel wire, at which a weight may be hung to produce equal strains in both wires. Young's modulus for brass \( = {10^{11}}N{m^{ - 2}}\) and Young's modulus for steel \(=2 \times 10^{11} {~N} {~m}^{-2}\).
supporting img

1 \(1\,m\)
2 \(3\,m\)
3 \(7\,m\)
4 \(9\,m\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369728 For a given material, the Young's modulus is 2.4 times that of rigidity modulus, then Poisson's ratio is

1 \(0.2{\rm{ }}\)
2 \(0.4{\rm{ }}\)
3 \(1.2{\rm{ }}\)
4 \(2.4\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369729 The relationship between Young's modulus \(Y\), bulk modulus \(B\) and modulus of rigidity \(\eta\) is

1 \(Y=\dfrac{9 \eta B}{\eta+3 B}\)
2 \(\eta=\dfrac{9 Y B}{Y+3 B}\)
3 \(Y=\dfrac{9 \eta B}{3 \eta+B}\)
4 \(Y=\dfrac{3 \eta B}{9 \eta+B}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369730 Two wires of equal lengths and cross-section areas are suspended, as shown in the figure. If their respective Young's moduli are \({Y_{1}}\) and \({Y_{2}}\), then the equivalent Young's modulus will be
supporting img

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

369731 Identify the incorrect statement.

1 Bulk modulus is relevant for solids, liquids and gases
2 Young's modulus and shear modulus are relevant only for solids.
3 Shear modulus for liquids is infinity
4 Metals have large values of Young's modulus than elastomers
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369732 A light rod of length 2 \(m\) is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of steel and is of cross-section \(10^{-3} {~m}^{2}\) and the other is of brass of cross-section \(2 \times 10^{-3} {~m}^{2}\). Find out the distance along the rod from steel wire, at which a weight may be hung to produce equal strains in both wires. Young's modulus for brass \( = {10^{11}}N{m^{ - 2}}\) and Young's modulus for steel \(=2 \times 10^{11} {~N} {~m}^{-2}\).
supporting img

1 \(1\,m\)
2 \(3\,m\)
3 \(7\,m\)
4 \(9\,m\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369728 For a given material, the Young's modulus is 2.4 times that of rigidity modulus, then Poisson's ratio is

1 \(0.2{\rm{ }}\)
2 \(0.4{\rm{ }}\)
3 \(1.2{\rm{ }}\)
4 \(2.4\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369729 The relationship between Young's modulus \(Y\), bulk modulus \(B\) and modulus of rigidity \(\eta\) is

1 \(Y=\dfrac{9 \eta B}{\eta+3 B}\)
2 \(\eta=\dfrac{9 Y B}{Y+3 B}\)
3 \(Y=\dfrac{9 \eta B}{3 \eta+B}\)
4 \(Y=\dfrac{3 \eta B}{9 \eta+B}\)
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369730 Two wires of equal lengths and cross-section areas are suspended, as shown in the figure. If their respective Young's moduli are \({Y_{1}}\) and \({Y_{2}}\), then the equivalent Young's modulus will be
supporting img

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

369731 Identify the incorrect statement.

1 Bulk modulus is relevant for solids, liquids and gases
2 Young's modulus and shear modulus are relevant only for solids.
3 Shear modulus for liquids is infinity
4 Metals have large values of Young's modulus than elastomers
PHXI09:MECHANICAL PROPERTIES OF SOLIDS

369732 A light rod of length 2 \(m\) is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of steel and is of cross-section \(10^{-3} {~m}^{2}\) and the other is of brass of cross-section \(2 \times 10^{-3} {~m}^{2}\). Find out the distance along the rod from steel wire, at which a weight may be hung to produce equal strains in both wires. Young's modulus for brass \( = {10^{11}}N{m^{ - 2}}\) and Young's modulus for steel \(=2 \times 10^{11} {~N} {~m}^{-2}\).
supporting img

1 \(1\,m\)
2 \(3\,m\)
3 \(7\,m\)
4 \(9\,m\)