01. Young's Modulus and Bulk Modulus and Change in Length
Mechanical Properties of Solids

141002 A steel wire of length $1.5 \mathrm{~m}$ and $3.0 \mathrm{~mm}^{2}$ crosssection area at $30^{\circ} \mathrm{C}$ is held straight (but under no tension) by attaching the ends to two walls. The coefficient of linear expansion for the wire is $1.0 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ and Young's modulus is $2 \times$ $10^{11} \mathrm{~N} / \mathrm{m}^{2}$. It the temperature of the wire is decreased to $-10^{\circ} \mathrm{C}$, the total tension in the wire will change by

1 $240 \mathrm{~N}$
2 $130 \mathrm{~N}$
3 $330 \mathrm{~N}$
4 $180 \mathrm{~N}$
Mechanical Properties of Solids

141003 Two wires of equal length and equal cross sectional areas are suspended as shown in the figure. Their Young's modulii are $Y_{1}$ and $Y_{2}$, respectively. The equivalent Young's modulus is

1 $\mathrm{Y}_{1}+\mathrm{Y}_{2}$
2 $\frac{Y_{1}+Y_{2}}{2}$
3 $\frac{\mathrm{Y}_{1} \mathrm{Y}_{2}}{\mathrm{Y}_{1}+\mathrm{Y}_{2}}$
4 $\sqrt{Y_{1} Y_{2}}$
Mechanical Properties of Solids

141004 The following four wires are made of the same material. If same tension is applied to each, the wire having largest extension is

1 length $0.5 \mathrm{~m}$, diameter $0.5 \mathrm{~mm}$.
2 length $1 \mathrm{~m}$, diameter $1 \mathrm{~mm}$.
3 length $2 \mathrm{~m}$, diameter $2 \mathrm{~mm}$.
4 length $3 \mathrm{~m}$, diameter $3 \mathrm{~mm}$.
Mechanical Properties of Solids

141005 A one metre steel wire of negligible mass and area of cross-section $0.01 \mathrm{~cm}^{2}$ is kept on a smooth horizontal table with one end fixed. A ball of mass $1 \mathrm{~kg}$ is attached to the other end. The ball and the wire are rotating with an angular velocity of $\omega$. If the elongation of the wire is $2 \mathrm{~mm}$, then $\omega$ is
(Young's modulus of steel $=2 \times 10^{11} \mathrm{Nm}^{-2}$ )

1 $5 \mathrm{rad} \mathrm{s}^{-1}$
2 $10 \mathrm{rad} \mathrm{s}^{-1}$
3 $15 \mathrm{rad} \mathrm{s}^{-1}$
4 $20 \mathrm{rad} \mathrm{s}^{-1}$
Mechanical Properties of Solids

141006 A solid copper cube of $7 \mathrm{~cm}$ edge is subjected to a hydraulic pressure of $8000 \mathrm{kPa}$. The volume contraction of the copper cube is (Bulk modulus of copper $=140 \mathrm{GPa})$

1 $196 \times 10^{-3} \mathrm{~cm}^{3}$
2 $19.6 \times 10^{-6} \mathrm{~cm}^{3}$
3 $19.6 \times 10^{-3} \mathrm{~cm}^{3}$
4 $196 \times 10^{3} \mathrm{~cm}^{3}$
Mechanical Properties of Solids

141002 A steel wire of length $1.5 \mathrm{~m}$ and $3.0 \mathrm{~mm}^{2}$ crosssection area at $30^{\circ} \mathrm{C}$ is held straight (but under no tension) by attaching the ends to two walls. The coefficient of linear expansion for the wire is $1.0 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ and Young's modulus is $2 \times$ $10^{11} \mathrm{~N} / \mathrm{m}^{2}$. It the temperature of the wire is decreased to $-10^{\circ} \mathrm{C}$, the total tension in the wire will change by

1 $240 \mathrm{~N}$
2 $130 \mathrm{~N}$
3 $330 \mathrm{~N}$
4 $180 \mathrm{~N}$
Mechanical Properties of Solids

141003 Two wires of equal length and equal cross sectional areas are suspended as shown in the figure. Their Young's modulii are $Y_{1}$ and $Y_{2}$, respectively. The equivalent Young's modulus is

1 $\mathrm{Y}_{1}+\mathrm{Y}_{2}$
2 $\frac{Y_{1}+Y_{2}}{2}$
3 $\frac{\mathrm{Y}_{1} \mathrm{Y}_{2}}{\mathrm{Y}_{1}+\mathrm{Y}_{2}}$
4 $\sqrt{Y_{1} Y_{2}}$
Mechanical Properties of Solids

141004 The following four wires are made of the same material. If same tension is applied to each, the wire having largest extension is

1 length $0.5 \mathrm{~m}$, diameter $0.5 \mathrm{~mm}$.
2 length $1 \mathrm{~m}$, diameter $1 \mathrm{~mm}$.
3 length $2 \mathrm{~m}$, diameter $2 \mathrm{~mm}$.
4 length $3 \mathrm{~m}$, diameter $3 \mathrm{~mm}$.
Mechanical Properties of Solids

141005 A one metre steel wire of negligible mass and area of cross-section $0.01 \mathrm{~cm}^{2}$ is kept on a smooth horizontal table with one end fixed. A ball of mass $1 \mathrm{~kg}$ is attached to the other end. The ball and the wire are rotating with an angular velocity of $\omega$. If the elongation of the wire is $2 \mathrm{~mm}$, then $\omega$ is
(Young's modulus of steel $=2 \times 10^{11} \mathrm{Nm}^{-2}$ )

1 $5 \mathrm{rad} \mathrm{s}^{-1}$
2 $10 \mathrm{rad} \mathrm{s}^{-1}$
3 $15 \mathrm{rad} \mathrm{s}^{-1}$
4 $20 \mathrm{rad} \mathrm{s}^{-1}$
Mechanical Properties of Solids

141006 A solid copper cube of $7 \mathrm{~cm}$ edge is subjected to a hydraulic pressure of $8000 \mathrm{kPa}$. The volume contraction of the copper cube is (Bulk modulus of copper $=140 \mathrm{GPa})$

1 $196 \times 10^{-3} \mathrm{~cm}^{3}$
2 $19.6 \times 10^{-6} \mathrm{~cm}^{3}$
3 $19.6 \times 10^{-3} \mathrm{~cm}^{3}$
4 $196 \times 10^{3} \mathrm{~cm}^{3}$
Mechanical Properties of Solids

141002 A steel wire of length $1.5 \mathrm{~m}$ and $3.0 \mathrm{~mm}^{2}$ crosssection area at $30^{\circ} \mathrm{C}$ is held straight (but under no tension) by attaching the ends to two walls. The coefficient of linear expansion for the wire is $1.0 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ and Young's modulus is $2 \times$ $10^{11} \mathrm{~N} / \mathrm{m}^{2}$. It the temperature of the wire is decreased to $-10^{\circ} \mathrm{C}$, the total tension in the wire will change by

1 $240 \mathrm{~N}$
2 $130 \mathrm{~N}$
3 $330 \mathrm{~N}$
4 $180 \mathrm{~N}$
Mechanical Properties of Solids

141003 Two wires of equal length and equal cross sectional areas are suspended as shown in the figure. Their Young's modulii are $Y_{1}$ and $Y_{2}$, respectively. The equivalent Young's modulus is

1 $\mathrm{Y}_{1}+\mathrm{Y}_{2}$
2 $\frac{Y_{1}+Y_{2}}{2}$
3 $\frac{\mathrm{Y}_{1} \mathrm{Y}_{2}}{\mathrm{Y}_{1}+\mathrm{Y}_{2}}$
4 $\sqrt{Y_{1} Y_{2}}$
Mechanical Properties of Solids

141004 The following four wires are made of the same material. If same tension is applied to each, the wire having largest extension is

1 length $0.5 \mathrm{~m}$, diameter $0.5 \mathrm{~mm}$.
2 length $1 \mathrm{~m}$, diameter $1 \mathrm{~mm}$.
3 length $2 \mathrm{~m}$, diameter $2 \mathrm{~mm}$.
4 length $3 \mathrm{~m}$, diameter $3 \mathrm{~mm}$.
Mechanical Properties of Solids

141005 A one metre steel wire of negligible mass and area of cross-section $0.01 \mathrm{~cm}^{2}$ is kept on a smooth horizontal table with one end fixed. A ball of mass $1 \mathrm{~kg}$ is attached to the other end. The ball and the wire are rotating with an angular velocity of $\omega$. If the elongation of the wire is $2 \mathrm{~mm}$, then $\omega$ is
(Young's modulus of steel $=2 \times 10^{11} \mathrm{Nm}^{-2}$ )

1 $5 \mathrm{rad} \mathrm{s}^{-1}$
2 $10 \mathrm{rad} \mathrm{s}^{-1}$
3 $15 \mathrm{rad} \mathrm{s}^{-1}$
4 $20 \mathrm{rad} \mathrm{s}^{-1}$
Mechanical Properties of Solids

141006 A solid copper cube of $7 \mathrm{~cm}$ edge is subjected to a hydraulic pressure of $8000 \mathrm{kPa}$. The volume contraction of the copper cube is (Bulk modulus of copper $=140 \mathrm{GPa})$

1 $196 \times 10^{-3} \mathrm{~cm}^{3}$
2 $19.6 \times 10^{-6} \mathrm{~cm}^{3}$
3 $19.6 \times 10^{-3} \mathrm{~cm}^{3}$
4 $196 \times 10^{3} \mathrm{~cm}^{3}$
Mechanical Properties of Solids

141002 A steel wire of length $1.5 \mathrm{~m}$ and $3.0 \mathrm{~mm}^{2}$ crosssection area at $30^{\circ} \mathrm{C}$ is held straight (but under no tension) by attaching the ends to two walls. The coefficient of linear expansion for the wire is $1.0 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ and Young's modulus is $2 \times$ $10^{11} \mathrm{~N} / \mathrm{m}^{2}$. It the temperature of the wire is decreased to $-10^{\circ} \mathrm{C}$, the total tension in the wire will change by

1 $240 \mathrm{~N}$
2 $130 \mathrm{~N}$
3 $330 \mathrm{~N}$
4 $180 \mathrm{~N}$
Mechanical Properties of Solids

141003 Two wires of equal length and equal cross sectional areas are suspended as shown in the figure. Their Young's modulii are $Y_{1}$ and $Y_{2}$, respectively. The equivalent Young's modulus is

1 $\mathrm{Y}_{1}+\mathrm{Y}_{2}$
2 $\frac{Y_{1}+Y_{2}}{2}$
3 $\frac{\mathrm{Y}_{1} \mathrm{Y}_{2}}{\mathrm{Y}_{1}+\mathrm{Y}_{2}}$
4 $\sqrt{Y_{1} Y_{2}}$
Mechanical Properties of Solids

141004 The following four wires are made of the same material. If same tension is applied to each, the wire having largest extension is

1 length $0.5 \mathrm{~m}$, diameter $0.5 \mathrm{~mm}$.
2 length $1 \mathrm{~m}$, diameter $1 \mathrm{~mm}$.
3 length $2 \mathrm{~m}$, diameter $2 \mathrm{~mm}$.
4 length $3 \mathrm{~m}$, diameter $3 \mathrm{~mm}$.
Mechanical Properties of Solids

141005 A one metre steel wire of negligible mass and area of cross-section $0.01 \mathrm{~cm}^{2}$ is kept on a smooth horizontal table with one end fixed. A ball of mass $1 \mathrm{~kg}$ is attached to the other end. The ball and the wire are rotating with an angular velocity of $\omega$. If the elongation of the wire is $2 \mathrm{~mm}$, then $\omega$ is
(Young's modulus of steel $=2 \times 10^{11} \mathrm{Nm}^{-2}$ )

1 $5 \mathrm{rad} \mathrm{s}^{-1}$
2 $10 \mathrm{rad} \mathrm{s}^{-1}$
3 $15 \mathrm{rad} \mathrm{s}^{-1}$
4 $20 \mathrm{rad} \mathrm{s}^{-1}$
Mechanical Properties of Solids

141006 A solid copper cube of $7 \mathrm{~cm}$ edge is subjected to a hydraulic pressure of $8000 \mathrm{kPa}$. The volume contraction of the copper cube is (Bulk modulus of copper $=140 \mathrm{GPa})$

1 $196 \times 10^{-3} \mathrm{~cm}^{3}$
2 $19.6 \times 10^{-6} \mathrm{~cm}^{3}$
3 $19.6 \times 10^{-3} \mathrm{~cm}^{3}$
4 $196 \times 10^{3} \mathrm{~cm}^{3}$
Mechanical Properties of Solids

141002 A steel wire of length $1.5 \mathrm{~m}$ and $3.0 \mathrm{~mm}^{2}$ crosssection area at $30^{\circ} \mathrm{C}$ is held straight (but under no tension) by attaching the ends to two walls. The coefficient of linear expansion for the wire is $1.0 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ and Young's modulus is $2 \times$ $10^{11} \mathrm{~N} / \mathrm{m}^{2}$. It the temperature of the wire is decreased to $-10^{\circ} \mathrm{C}$, the total tension in the wire will change by

1 $240 \mathrm{~N}$
2 $130 \mathrm{~N}$
3 $330 \mathrm{~N}$
4 $180 \mathrm{~N}$
Mechanical Properties of Solids

141003 Two wires of equal length and equal cross sectional areas are suspended as shown in the figure. Their Young's modulii are $Y_{1}$ and $Y_{2}$, respectively. The equivalent Young's modulus is

1 $\mathrm{Y}_{1}+\mathrm{Y}_{2}$
2 $\frac{Y_{1}+Y_{2}}{2}$
3 $\frac{\mathrm{Y}_{1} \mathrm{Y}_{2}}{\mathrm{Y}_{1}+\mathrm{Y}_{2}}$
4 $\sqrt{Y_{1} Y_{2}}$
Mechanical Properties of Solids

141004 The following four wires are made of the same material. If same tension is applied to each, the wire having largest extension is

1 length $0.5 \mathrm{~m}$, diameter $0.5 \mathrm{~mm}$.
2 length $1 \mathrm{~m}$, diameter $1 \mathrm{~mm}$.
3 length $2 \mathrm{~m}$, diameter $2 \mathrm{~mm}$.
4 length $3 \mathrm{~m}$, diameter $3 \mathrm{~mm}$.
Mechanical Properties of Solids

141005 A one metre steel wire of negligible mass and area of cross-section $0.01 \mathrm{~cm}^{2}$ is kept on a smooth horizontal table with one end fixed. A ball of mass $1 \mathrm{~kg}$ is attached to the other end. The ball and the wire are rotating with an angular velocity of $\omega$. If the elongation of the wire is $2 \mathrm{~mm}$, then $\omega$ is
(Young's modulus of steel $=2 \times 10^{11} \mathrm{Nm}^{-2}$ )

1 $5 \mathrm{rad} \mathrm{s}^{-1}$
2 $10 \mathrm{rad} \mathrm{s}^{-1}$
3 $15 \mathrm{rad} \mathrm{s}^{-1}$
4 $20 \mathrm{rad} \mathrm{s}^{-1}$
Mechanical Properties of Solids

141006 A solid copper cube of $7 \mathrm{~cm}$ edge is subjected to a hydraulic pressure of $8000 \mathrm{kPa}$. The volume contraction of the copper cube is (Bulk modulus of copper $=140 \mathrm{GPa})$

1 $196 \times 10^{-3} \mathrm{~cm}^{3}$
2 $19.6 \times 10^{-6} \mathrm{~cm}^{3}$
3 $19.6 \times 10^{-3} \mathrm{~cm}^{3}$
4 $196 \times 10^{3} \mathrm{~cm}^{3}$