00. Elasticity, Stress, Strain and Hooke's law
Mechanical Properties of Solids

140940 The temperature of a steel rod placed between rigid supports and of length $L$, area of crosssection A, Young's Modulus $Y$ and coefficient of linear expansion $\alpha$, is raised by $T$. The amount of work done when heated is

1 $\frac{\mathrm{YA} \alpha \mathrm{T}^{2} \mathrm{~L}}{2}$
2 $\frac{Y A \alpha^{2} T^{2} L}{2}$
3 $\frac{Y A \alpha T L}{2}$
4 $\frac{\mathrm{YA}^{2} \alpha^{2} \mathrm{~T}^{2} \ell^{2}}{2}$
Mechanical Properties of Solids

140941 Assertion: Strain causes the stress in an elastic body.
Reason: An elastic rubber is more plastic in nature.

1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Mechanical Properties of Solids

140942 A copper wire (young's modulus : $110 \times 10^{9}$ $\mathrm{N} / \mathrm{m}^{2}$ ) having the length of $2 \mathrm{~m}$ and the cross sectional area of $0.5 \mathrm{~cm}^{2}$ is stretched to increase its length by $0.1 \%$. The required force is

1 $2750 \mathrm{~N}$
2 $27500 \mathrm{~N}$
3 $55000 \mathrm{~N}$
4 $5500 \mathrm{~N}$
Mechanical Properties of Solids

140943 A steel wire of length $1.5 \mathrm{~m}$ can withstand a maximum $1500 \mathrm{~N}$ tension before it breaks. The tensile strength of steel is $5 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$. If the same wire is stretched by $0.20 \mathrm{~cm}$ in the elastic limit, the tension in the wire is (Young's modulus of steel $2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$ )

1 $750 \mathrm{~N}$
2 $800 \mathrm{~N}$
3 $225 \mathrm{~N}$
4 $1250 \mathrm{~N}$
Mechanical Properties of Solids

140944 A steel wire of length $20 \mathrm{~cm}$ and area of crosssection $1 \mathrm{~mm}^{2}$ is tied rigidly at both the ends. When the temperature of the wire is changed from $40^{\circ} \mathrm{C}$ to $20^{\circ} \mathrm{C}$, find the change in its tension. Given, the coefficient of linear expansion for steel is $1.1 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$ and Young's modulus of steel is $2.0 \times 10^{11} \mathrm{Nm}^{-2}$.

1 $22 \mathrm{~N}$
2 $44 \mathrm{~N}$
3 $16 \mathrm{~N}$
4 $8 \mathrm{~N}$
Mechanical Properties of Solids

140940 The temperature of a steel rod placed between rigid supports and of length $L$, area of crosssection A, Young's Modulus $Y$ and coefficient of linear expansion $\alpha$, is raised by $T$. The amount of work done when heated is

1 $\frac{\mathrm{YA} \alpha \mathrm{T}^{2} \mathrm{~L}}{2}$
2 $\frac{Y A \alpha^{2} T^{2} L}{2}$
3 $\frac{Y A \alpha T L}{2}$
4 $\frac{\mathrm{YA}^{2} \alpha^{2} \mathrm{~T}^{2} \ell^{2}}{2}$
Mechanical Properties of Solids

140941 Assertion: Strain causes the stress in an elastic body.
Reason: An elastic rubber is more plastic in nature.

1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Mechanical Properties of Solids

140942 A copper wire (young's modulus : $110 \times 10^{9}$ $\mathrm{N} / \mathrm{m}^{2}$ ) having the length of $2 \mathrm{~m}$ and the cross sectional area of $0.5 \mathrm{~cm}^{2}$ is stretched to increase its length by $0.1 \%$. The required force is

1 $2750 \mathrm{~N}$
2 $27500 \mathrm{~N}$
3 $55000 \mathrm{~N}$
4 $5500 \mathrm{~N}$
Mechanical Properties of Solids

140943 A steel wire of length $1.5 \mathrm{~m}$ can withstand a maximum $1500 \mathrm{~N}$ tension before it breaks. The tensile strength of steel is $5 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$. If the same wire is stretched by $0.20 \mathrm{~cm}$ in the elastic limit, the tension in the wire is (Young's modulus of steel $2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$ )

1 $750 \mathrm{~N}$
2 $800 \mathrm{~N}$
3 $225 \mathrm{~N}$
4 $1250 \mathrm{~N}$
Mechanical Properties of Solids

140944 A steel wire of length $20 \mathrm{~cm}$ and area of crosssection $1 \mathrm{~mm}^{2}$ is tied rigidly at both the ends. When the temperature of the wire is changed from $40^{\circ} \mathrm{C}$ to $20^{\circ} \mathrm{C}$, find the change in its tension. Given, the coefficient of linear expansion for steel is $1.1 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$ and Young's modulus of steel is $2.0 \times 10^{11} \mathrm{Nm}^{-2}$.

1 $22 \mathrm{~N}$
2 $44 \mathrm{~N}$
3 $16 \mathrm{~N}$
4 $8 \mathrm{~N}$
Mechanical Properties of Solids

140940 The temperature of a steel rod placed between rigid supports and of length $L$, area of crosssection A, Young's Modulus $Y$ and coefficient of linear expansion $\alpha$, is raised by $T$. The amount of work done when heated is

1 $\frac{\mathrm{YA} \alpha \mathrm{T}^{2} \mathrm{~L}}{2}$
2 $\frac{Y A \alpha^{2} T^{2} L}{2}$
3 $\frac{Y A \alpha T L}{2}$
4 $\frac{\mathrm{YA}^{2} \alpha^{2} \mathrm{~T}^{2} \ell^{2}}{2}$
Mechanical Properties of Solids

140941 Assertion: Strain causes the stress in an elastic body.
Reason: An elastic rubber is more plastic in nature.

1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Mechanical Properties of Solids

140942 A copper wire (young's modulus : $110 \times 10^{9}$ $\mathrm{N} / \mathrm{m}^{2}$ ) having the length of $2 \mathrm{~m}$ and the cross sectional area of $0.5 \mathrm{~cm}^{2}$ is stretched to increase its length by $0.1 \%$. The required force is

1 $2750 \mathrm{~N}$
2 $27500 \mathrm{~N}$
3 $55000 \mathrm{~N}$
4 $5500 \mathrm{~N}$
Mechanical Properties of Solids

140943 A steel wire of length $1.5 \mathrm{~m}$ can withstand a maximum $1500 \mathrm{~N}$ tension before it breaks. The tensile strength of steel is $5 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$. If the same wire is stretched by $0.20 \mathrm{~cm}$ in the elastic limit, the tension in the wire is (Young's modulus of steel $2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$ )

1 $750 \mathrm{~N}$
2 $800 \mathrm{~N}$
3 $225 \mathrm{~N}$
4 $1250 \mathrm{~N}$
Mechanical Properties of Solids

140944 A steel wire of length $20 \mathrm{~cm}$ and area of crosssection $1 \mathrm{~mm}^{2}$ is tied rigidly at both the ends. When the temperature of the wire is changed from $40^{\circ} \mathrm{C}$ to $20^{\circ} \mathrm{C}$, find the change in its tension. Given, the coefficient of linear expansion for steel is $1.1 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$ and Young's modulus of steel is $2.0 \times 10^{11} \mathrm{Nm}^{-2}$.

1 $22 \mathrm{~N}$
2 $44 \mathrm{~N}$
3 $16 \mathrm{~N}$
4 $8 \mathrm{~N}$
Mechanical Properties of Solids

140940 The temperature of a steel rod placed between rigid supports and of length $L$, area of crosssection A, Young's Modulus $Y$ and coefficient of linear expansion $\alpha$, is raised by $T$. The amount of work done when heated is

1 $\frac{\mathrm{YA} \alpha \mathrm{T}^{2} \mathrm{~L}}{2}$
2 $\frac{Y A \alpha^{2} T^{2} L}{2}$
3 $\frac{Y A \alpha T L}{2}$
4 $\frac{\mathrm{YA}^{2} \alpha^{2} \mathrm{~T}^{2} \ell^{2}}{2}$
Mechanical Properties of Solids

140941 Assertion: Strain causes the stress in an elastic body.
Reason: An elastic rubber is more plastic in nature.

1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Mechanical Properties of Solids

140942 A copper wire (young's modulus : $110 \times 10^{9}$ $\mathrm{N} / \mathrm{m}^{2}$ ) having the length of $2 \mathrm{~m}$ and the cross sectional area of $0.5 \mathrm{~cm}^{2}$ is stretched to increase its length by $0.1 \%$. The required force is

1 $2750 \mathrm{~N}$
2 $27500 \mathrm{~N}$
3 $55000 \mathrm{~N}$
4 $5500 \mathrm{~N}$
Mechanical Properties of Solids

140943 A steel wire of length $1.5 \mathrm{~m}$ can withstand a maximum $1500 \mathrm{~N}$ tension before it breaks. The tensile strength of steel is $5 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$. If the same wire is stretched by $0.20 \mathrm{~cm}$ in the elastic limit, the tension in the wire is (Young's modulus of steel $2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$ )

1 $750 \mathrm{~N}$
2 $800 \mathrm{~N}$
3 $225 \mathrm{~N}$
4 $1250 \mathrm{~N}$
Mechanical Properties of Solids

140944 A steel wire of length $20 \mathrm{~cm}$ and area of crosssection $1 \mathrm{~mm}^{2}$ is tied rigidly at both the ends. When the temperature of the wire is changed from $40^{\circ} \mathrm{C}$ to $20^{\circ} \mathrm{C}$, find the change in its tension. Given, the coefficient of linear expansion for steel is $1.1 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$ and Young's modulus of steel is $2.0 \times 10^{11} \mathrm{Nm}^{-2}$.

1 $22 \mathrm{~N}$
2 $44 \mathrm{~N}$
3 $16 \mathrm{~N}$
4 $8 \mathrm{~N}$
Mechanical Properties of Solids

140940 The temperature of a steel rod placed between rigid supports and of length $L$, area of crosssection A, Young's Modulus $Y$ and coefficient of linear expansion $\alpha$, is raised by $T$. The amount of work done when heated is

1 $\frac{\mathrm{YA} \alpha \mathrm{T}^{2} \mathrm{~L}}{2}$
2 $\frac{Y A \alpha^{2} T^{2} L}{2}$
3 $\frac{Y A \alpha T L}{2}$
4 $\frac{\mathrm{YA}^{2} \alpha^{2} \mathrm{~T}^{2} \ell^{2}}{2}$
Mechanical Properties of Solids

140941 Assertion: Strain causes the stress in an elastic body.
Reason: An elastic rubber is more plastic in nature.

1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Mechanical Properties of Solids

140942 A copper wire (young's modulus : $110 \times 10^{9}$ $\mathrm{N} / \mathrm{m}^{2}$ ) having the length of $2 \mathrm{~m}$ and the cross sectional area of $0.5 \mathrm{~cm}^{2}$ is stretched to increase its length by $0.1 \%$. The required force is

1 $2750 \mathrm{~N}$
2 $27500 \mathrm{~N}$
3 $55000 \mathrm{~N}$
4 $5500 \mathrm{~N}$
Mechanical Properties of Solids

140943 A steel wire of length $1.5 \mathrm{~m}$ can withstand a maximum $1500 \mathrm{~N}$ tension before it breaks. The tensile strength of steel is $5 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$. If the same wire is stretched by $0.20 \mathrm{~cm}$ in the elastic limit, the tension in the wire is (Young's modulus of steel $2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$ )

1 $750 \mathrm{~N}$
2 $800 \mathrm{~N}$
3 $225 \mathrm{~N}$
4 $1250 \mathrm{~N}$
Mechanical Properties of Solids

140944 A steel wire of length $20 \mathrm{~cm}$ and area of crosssection $1 \mathrm{~mm}^{2}$ is tied rigidly at both the ends. When the temperature of the wire is changed from $40^{\circ} \mathrm{C}$ to $20^{\circ} \mathrm{C}$, find the change in its tension. Given, the coefficient of linear expansion for steel is $1.1 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$ and Young's modulus of steel is $2.0 \times 10^{11} \mathrm{Nm}^{-2}$.

1 $22 \mathrm{~N}$
2 $44 \mathrm{~N}$
3 $16 \mathrm{~N}$
4 $8 \mathrm{~N}$