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

140974 The length of a metal wire is $L$, when it is subjected to tension $T$. If the tension is increased to $T+\Delta T$, the length becomes $L+$ $\Delta L$. The natural length of the wire is

1 $\frac{\mathrm{L}(\Delta \mathrm{T})-(\Delta \mathrm{L}) \mathrm{T}}{\Delta \mathrm{T}}$
2 $\mathrm{L}-2 \Delta \mathrm{L}$
3 $\Delta \mathrm{L}\left(\frac{\Delta \mathrm{T}}{\mathrm{T}}\right)$
4 $\frac{\mathrm{T}(\Delta \mathrm{L})-\mathrm{L}(\Delta \mathrm{T})}{\Delta \mathrm{T}}$
Mechanical Properties of Solids

140976 The area of cross-section of a wire of length 2.1 $\mathrm{m}$ is $2 \mathrm{~mm}^{2}$. Find the increase in its length when it is loaded with $0.5 \mathrm{~kg}$. The Young's Modulus of material of wire is $11 \times 10^{10} \mathrm{Nm}^{-2}$. $(\mathrm{g}$ $=10 \mathrm{~m} \mathrm{~s}^{-2}$ )

1 $0.1 \mathrm{~mm}$
2 $47.73 \mu \mathrm{m}$
3 $0.1 \mu \mathrm{m}$
4 $47.73 \mathrm{~mm}$
Mechanical Properties of Solids

140977 At $50^{\circ} \mathrm{C}$ a brass rod and a steel rod of equal length $50 \mathrm{~cm}$ each and equal diameters are joined together. The composite rod is heated to $250^{\circ} \mathrm{C}$. Find the change in length of the composite rod. $\left[\alpha_{\text {Brass }}=20 \times 10^{-6}{ }^{\circ} \mathrm{C}^{-1}\right.$ and $\alpha_{\text {steel }}$ $=12 \times 10^{-6}{ }^{0} \mathrm{C}^{-1}$ ]

1 $0.28 \mathrm{~cm}$
2 $0.32 \mathrm{~cm}$
3 $0.30 \mathrm{~cm}$
4 $0.20 \mathrm{~cm}$
Mechanical Properties of Solids

140978 Young's modulus of a wire is $2 \times 10^{11} \mathrm{~N} \cdot \mathrm{m}^{-2}$. If an external stretching force of $2 \times 10^{11} \mathrm{~N}$ is applied to a wire of length $L$. The final length of the wire is - (cross-section $=$ unity $)$

1 $2 \mathrm{~L}$
2 $1.5 \mathrm{~L}$
3 $3 \mathrm{~L}$
4 $1.25 \mathrm{~L}$
Mechanical Properties of Solids

140974 The length of a metal wire is $L$, when it is subjected to tension $T$. If the tension is increased to $T+\Delta T$, the length becomes $L+$ $\Delta L$. The natural length of the wire is

1 $\frac{\mathrm{L}(\Delta \mathrm{T})-(\Delta \mathrm{L}) \mathrm{T}}{\Delta \mathrm{T}}$
2 $\mathrm{L}-2 \Delta \mathrm{L}$
3 $\Delta \mathrm{L}\left(\frac{\Delta \mathrm{T}}{\mathrm{T}}\right)$
4 $\frac{\mathrm{T}(\Delta \mathrm{L})-\mathrm{L}(\Delta \mathrm{T})}{\Delta \mathrm{T}}$
Mechanical Properties of Solids

140976 The area of cross-section of a wire of length 2.1 $\mathrm{m}$ is $2 \mathrm{~mm}^{2}$. Find the increase in its length when it is loaded with $0.5 \mathrm{~kg}$. The Young's Modulus of material of wire is $11 \times 10^{10} \mathrm{Nm}^{-2}$. $(\mathrm{g}$ $=10 \mathrm{~m} \mathrm{~s}^{-2}$ )

1 $0.1 \mathrm{~mm}$
2 $47.73 \mu \mathrm{m}$
3 $0.1 \mu \mathrm{m}$
4 $47.73 \mathrm{~mm}$
Mechanical Properties of Solids

140977 At $50^{\circ} \mathrm{C}$ a brass rod and a steel rod of equal length $50 \mathrm{~cm}$ each and equal diameters are joined together. The composite rod is heated to $250^{\circ} \mathrm{C}$. Find the change in length of the composite rod. $\left[\alpha_{\text {Brass }}=20 \times 10^{-6}{ }^{\circ} \mathrm{C}^{-1}\right.$ and $\alpha_{\text {steel }}$ $=12 \times 10^{-6}{ }^{0} \mathrm{C}^{-1}$ ]

1 $0.28 \mathrm{~cm}$
2 $0.32 \mathrm{~cm}$
3 $0.30 \mathrm{~cm}$
4 $0.20 \mathrm{~cm}$
Mechanical Properties of Solids

140978 Young's modulus of a wire is $2 \times 10^{11} \mathrm{~N} \cdot \mathrm{m}^{-2}$. If an external stretching force of $2 \times 10^{11} \mathrm{~N}$ is applied to a wire of length $L$. The final length of the wire is - (cross-section $=$ unity $)$

1 $2 \mathrm{~L}$
2 $1.5 \mathrm{~L}$
3 $3 \mathrm{~L}$
4 $1.25 \mathrm{~L}$
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Mechanical Properties of Solids

140974 The length of a metal wire is $L$, when it is subjected to tension $T$. If the tension is increased to $T+\Delta T$, the length becomes $L+$ $\Delta L$. The natural length of the wire is

1 $\frac{\mathrm{L}(\Delta \mathrm{T})-(\Delta \mathrm{L}) \mathrm{T}}{\Delta \mathrm{T}}$
2 $\mathrm{L}-2 \Delta \mathrm{L}$
3 $\Delta \mathrm{L}\left(\frac{\Delta \mathrm{T}}{\mathrm{T}}\right)$
4 $\frac{\mathrm{T}(\Delta \mathrm{L})-\mathrm{L}(\Delta \mathrm{T})}{\Delta \mathrm{T}}$
Mechanical Properties of Solids

140976 The area of cross-section of a wire of length 2.1 $\mathrm{m}$ is $2 \mathrm{~mm}^{2}$. Find the increase in its length when it is loaded with $0.5 \mathrm{~kg}$. The Young's Modulus of material of wire is $11 \times 10^{10} \mathrm{Nm}^{-2}$. $(\mathrm{g}$ $=10 \mathrm{~m} \mathrm{~s}^{-2}$ )

1 $0.1 \mathrm{~mm}$
2 $47.73 \mu \mathrm{m}$
3 $0.1 \mu \mathrm{m}$
4 $47.73 \mathrm{~mm}$
Mechanical Properties of Solids

140977 At $50^{\circ} \mathrm{C}$ a brass rod and a steel rod of equal length $50 \mathrm{~cm}$ each and equal diameters are joined together. The composite rod is heated to $250^{\circ} \mathrm{C}$. Find the change in length of the composite rod. $\left[\alpha_{\text {Brass }}=20 \times 10^{-6}{ }^{\circ} \mathrm{C}^{-1}\right.$ and $\alpha_{\text {steel }}$ $=12 \times 10^{-6}{ }^{0} \mathrm{C}^{-1}$ ]

1 $0.28 \mathrm{~cm}$
2 $0.32 \mathrm{~cm}$
3 $0.30 \mathrm{~cm}$
4 $0.20 \mathrm{~cm}$
Mechanical Properties of Solids

140978 Young's modulus of a wire is $2 \times 10^{11} \mathrm{~N} \cdot \mathrm{m}^{-2}$. If an external stretching force of $2 \times 10^{11} \mathrm{~N}$ is applied to a wire of length $L$. The final length of the wire is - (cross-section $=$ unity $)$

1 $2 \mathrm{~L}$
2 $1.5 \mathrm{~L}$
3 $3 \mathrm{~L}$
4 $1.25 \mathrm{~L}$
Mechanical Properties of Solids

140974 The length of a metal wire is $L$, when it is subjected to tension $T$. If the tension is increased to $T+\Delta T$, the length becomes $L+$ $\Delta L$. The natural length of the wire is

1 $\frac{\mathrm{L}(\Delta \mathrm{T})-(\Delta \mathrm{L}) \mathrm{T}}{\Delta \mathrm{T}}$
2 $\mathrm{L}-2 \Delta \mathrm{L}$
3 $\Delta \mathrm{L}\left(\frac{\Delta \mathrm{T}}{\mathrm{T}}\right)$
4 $\frac{\mathrm{T}(\Delta \mathrm{L})-\mathrm{L}(\Delta \mathrm{T})}{\Delta \mathrm{T}}$
Mechanical Properties of Solids

140976 The area of cross-section of a wire of length 2.1 $\mathrm{m}$ is $2 \mathrm{~mm}^{2}$. Find the increase in its length when it is loaded with $0.5 \mathrm{~kg}$. The Young's Modulus of material of wire is $11 \times 10^{10} \mathrm{Nm}^{-2}$. $(\mathrm{g}$ $=10 \mathrm{~m} \mathrm{~s}^{-2}$ )

1 $0.1 \mathrm{~mm}$
2 $47.73 \mu \mathrm{m}$
3 $0.1 \mu \mathrm{m}$
4 $47.73 \mathrm{~mm}$
Mechanical Properties of Solids

140977 At $50^{\circ} \mathrm{C}$ a brass rod and a steel rod of equal length $50 \mathrm{~cm}$ each and equal diameters are joined together. The composite rod is heated to $250^{\circ} \mathrm{C}$. Find the change in length of the composite rod. $\left[\alpha_{\text {Brass }}=20 \times 10^{-6}{ }^{\circ} \mathrm{C}^{-1}\right.$ and $\alpha_{\text {steel }}$ $=12 \times 10^{-6}{ }^{0} \mathrm{C}^{-1}$ ]

1 $0.28 \mathrm{~cm}$
2 $0.32 \mathrm{~cm}$
3 $0.30 \mathrm{~cm}$
4 $0.20 \mathrm{~cm}$
Mechanical Properties of Solids

140978 Young's modulus of a wire is $2 \times 10^{11} \mathrm{~N} \cdot \mathrm{m}^{-2}$. If an external stretching force of $2 \times 10^{11} \mathrm{~N}$ is applied to a wire of length $L$. The final length of the wire is - (cross-section $=$ unity $)$

1 $2 \mathrm{~L}$
2 $1.5 \mathrm{~L}$
3 $3 \mathrm{~L}$
4 $1.25 \mathrm{~L}$