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

140962 Two wires $A$ and $B$ of same cross-section are connected end to end. When same tension is created in both wires, the elongation in $B$ wire is twice the elongation in $A$ wire. If $L_{A}$ and $L_{B}$ are the initial lengths of the wires $A$ and $B$ respectively then (Young's modulus of material of wire $A=2 \times 10^{11} \mathrm{Nm}^{-2}$ and Young's modulus of material of wire $B=1.1 \times 10^{11} \mathrm{Nm}^{-2}$ )

1 $\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{10}{11}$
2 $\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{4}{5}$
3 $\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{9}{11}$
4 $\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{3}{7}$
Mechanical Properties of Solids

140964 A steel wire of length $1.25 \mathrm{~m}$ is stretched between two rigid supports. The tension in the wire produces an elastic strain of $0.14 \%$. The fundamental frequency of the wire is
(Density and Young's modules of steel are $7.7 \times$ $10^{3} \mathrm{kgm}^{-3}$ and $2.2 \times 10^{11} \mathrm{Nm}^{-2}$ respectively)

1 $20 \mathrm{~Hz}$
2 $40 \mathrm{~Hz}$
3 $80 \mathrm{~Hz}$
4 $160 \mathrm{~Hz}$
Mechanical Properties of Solids

140965 One end of the steel rod is clamped to the stand and the other end is attached to a mass of 1000 $\mathrm{kg}$ as shown in the figure. The length of the rod is $50 \mathrm{~cm}$ and its cross-sectional area is 1000 $\mathrm{mm}^{2}$. The change in the length of the rod due to the weight of the mass is-
(Young's modulus of steel $=2 \times 10^{11} \mathrm{Nm}^{-2}$ and Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

1 $0.025 \mathrm{~mm}$
2 $0.10 \mathrm{~mm}$
3 $0.050 \mathrm{~mm}$
4 $0.075 \mathrm{~mm}$
Mechanical Properties of Solids

140966 A wire of length $L$ is hanging from a fixed supports. The length changes to $L_{1}$ and $L_{2}$ when masses $1 \mathrm{~kg}$ and $2 \mathrm{~kg}$ are suspended respectively from its free end. Then the value of $L$ is equal to

1 $\sqrt{\mathrm{L}_{1} \mathrm{~L}_{2}}$
2 $\frac{\mathrm{L}_{1}+\mathrm{L}_{2}}{2}$
3 $2 \mathrm{~L}_{1}-\mathrm{L}_{2}$
4 $3 \mathrm{~L}_{1}-2 \mathrm{~L}_{2}$
Mechanical Properties of Solids

140968 An object of mass $15 \mathrm{~kg}$ is attached to the end of a metal wire of unstretched length $1.0 \mathrm{~m}$. The object is then whirled in a vertical circle with an angular velocity of $4 \mathrm{rad} / \mathrm{s}$ at the bottom of the circle. If the cross sectional area of the wire is $0.05 \mathrm{~cm}^{2}$ and Young's modulus of metal is $2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$, then the elongation of the wire when the mass is at the lowest point of its path
(Take $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )

1 $0.27 \mathrm{~mm}$
2 $0.39 \mathrm{~mm}$
3 $0.55 \mathrm{~mm}$
4 $0.25 \mathrm{~mm}$
Mechanical Properties of Solids

140962 Two wires $A$ and $B$ of same cross-section are connected end to end. When same tension is created in both wires, the elongation in $B$ wire is twice the elongation in $A$ wire. If $L_{A}$ and $L_{B}$ are the initial lengths of the wires $A$ and $B$ respectively then (Young's modulus of material of wire $A=2 \times 10^{11} \mathrm{Nm}^{-2}$ and Young's modulus of material of wire $B=1.1 \times 10^{11} \mathrm{Nm}^{-2}$ )

1 $\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{10}{11}$
2 $\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{4}{5}$
3 $\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{9}{11}$
4 $\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{3}{7}$
Mechanical Properties of Solids

140964 A steel wire of length $1.25 \mathrm{~m}$ is stretched between two rigid supports. The tension in the wire produces an elastic strain of $0.14 \%$. The fundamental frequency of the wire is
(Density and Young's modules of steel are $7.7 \times$ $10^{3} \mathrm{kgm}^{-3}$ and $2.2 \times 10^{11} \mathrm{Nm}^{-2}$ respectively)

1 $20 \mathrm{~Hz}$
2 $40 \mathrm{~Hz}$
3 $80 \mathrm{~Hz}$
4 $160 \mathrm{~Hz}$
Mechanical Properties of Solids

140965 One end of the steel rod is clamped to the stand and the other end is attached to a mass of 1000 $\mathrm{kg}$ as shown in the figure. The length of the rod is $50 \mathrm{~cm}$ and its cross-sectional area is 1000 $\mathrm{mm}^{2}$. The change in the length of the rod due to the weight of the mass is-
(Young's modulus of steel $=2 \times 10^{11} \mathrm{Nm}^{-2}$ and Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

1 $0.025 \mathrm{~mm}$
2 $0.10 \mathrm{~mm}$
3 $0.050 \mathrm{~mm}$
4 $0.075 \mathrm{~mm}$
Mechanical Properties of Solids

140966 A wire of length $L$ is hanging from a fixed supports. The length changes to $L_{1}$ and $L_{2}$ when masses $1 \mathrm{~kg}$ and $2 \mathrm{~kg}$ are suspended respectively from its free end. Then the value of $L$ is equal to

1 $\sqrt{\mathrm{L}_{1} \mathrm{~L}_{2}}$
2 $\frac{\mathrm{L}_{1}+\mathrm{L}_{2}}{2}$
3 $2 \mathrm{~L}_{1}-\mathrm{L}_{2}$
4 $3 \mathrm{~L}_{1}-2 \mathrm{~L}_{2}$
Mechanical Properties of Solids

140968 An object of mass $15 \mathrm{~kg}$ is attached to the end of a metal wire of unstretched length $1.0 \mathrm{~m}$. The object is then whirled in a vertical circle with an angular velocity of $4 \mathrm{rad} / \mathrm{s}$ at the bottom of the circle. If the cross sectional area of the wire is $0.05 \mathrm{~cm}^{2}$ and Young's modulus of metal is $2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$, then the elongation of the wire when the mass is at the lowest point of its path
(Take $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )

1 $0.27 \mathrm{~mm}$
2 $0.39 \mathrm{~mm}$
3 $0.55 \mathrm{~mm}$
4 $0.25 \mathrm{~mm}$
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Mechanical Properties of Solids

140962 Two wires $A$ and $B$ of same cross-section are connected end to end. When same tension is created in both wires, the elongation in $B$ wire is twice the elongation in $A$ wire. If $L_{A}$ and $L_{B}$ are the initial lengths of the wires $A$ and $B$ respectively then (Young's modulus of material of wire $A=2 \times 10^{11} \mathrm{Nm}^{-2}$ and Young's modulus of material of wire $B=1.1 \times 10^{11} \mathrm{Nm}^{-2}$ )

1 $\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{10}{11}$
2 $\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{4}{5}$
3 $\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{9}{11}$
4 $\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{3}{7}$
Mechanical Properties of Solids

140964 A steel wire of length $1.25 \mathrm{~m}$ is stretched between two rigid supports. The tension in the wire produces an elastic strain of $0.14 \%$. The fundamental frequency of the wire is
(Density and Young's modules of steel are $7.7 \times$ $10^{3} \mathrm{kgm}^{-3}$ and $2.2 \times 10^{11} \mathrm{Nm}^{-2}$ respectively)

1 $20 \mathrm{~Hz}$
2 $40 \mathrm{~Hz}$
3 $80 \mathrm{~Hz}$
4 $160 \mathrm{~Hz}$
Mechanical Properties of Solids

140965 One end of the steel rod is clamped to the stand and the other end is attached to a mass of 1000 $\mathrm{kg}$ as shown in the figure. The length of the rod is $50 \mathrm{~cm}$ and its cross-sectional area is 1000 $\mathrm{mm}^{2}$. The change in the length of the rod due to the weight of the mass is-
(Young's modulus of steel $=2 \times 10^{11} \mathrm{Nm}^{-2}$ and Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

1 $0.025 \mathrm{~mm}$
2 $0.10 \mathrm{~mm}$
3 $0.050 \mathrm{~mm}$
4 $0.075 \mathrm{~mm}$
Mechanical Properties of Solids

140966 A wire of length $L$ is hanging from a fixed supports. The length changes to $L_{1}$ and $L_{2}$ when masses $1 \mathrm{~kg}$ and $2 \mathrm{~kg}$ are suspended respectively from its free end. Then the value of $L$ is equal to

1 $\sqrt{\mathrm{L}_{1} \mathrm{~L}_{2}}$
2 $\frac{\mathrm{L}_{1}+\mathrm{L}_{2}}{2}$
3 $2 \mathrm{~L}_{1}-\mathrm{L}_{2}$
4 $3 \mathrm{~L}_{1}-2 \mathrm{~L}_{2}$
Mechanical Properties of Solids

140968 An object of mass $15 \mathrm{~kg}$ is attached to the end of a metal wire of unstretched length $1.0 \mathrm{~m}$. The object is then whirled in a vertical circle with an angular velocity of $4 \mathrm{rad} / \mathrm{s}$ at the bottom of the circle. If the cross sectional area of the wire is $0.05 \mathrm{~cm}^{2}$ and Young's modulus of metal is $2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$, then the elongation of the wire when the mass is at the lowest point of its path
(Take $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )

1 $0.27 \mathrm{~mm}$
2 $0.39 \mathrm{~mm}$
3 $0.55 \mathrm{~mm}$
4 $0.25 \mathrm{~mm}$
Mechanical Properties of Solids

140962 Two wires $A$ and $B$ of same cross-section are connected end to end. When same tension is created in both wires, the elongation in $B$ wire is twice the elongation in $A$ wire. If $L_{A}$ and $L_{B}$ are the initial lengths of the wires $A$ and $B$ respectively then (Young's modulus of material of wire $A=2 \times 10^{11} \mathrm{Nm}^{-2}$ and Young's modulus of material of wire $B=1.1 \times 10^{11} \mathrm{Nm}^{-2}$ )

1 $\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{10}{11}$
2 $\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{4}{5}$
3 $\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{9}{11}$
4 $\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{3}{7}$
Mechanical Properties of Solids

140964 A steel wire of length $1.25 \mathrm{~m}$ is stretched between two rigid supports. The tension in the wire produces an elastic strain of $0.14 \%$. The fundamental frequency of the wire is
(Density and Young's modules of steel are $7.7 \times$ $10^{3} \mathrm{kgm}^{-3}$ and $2.2 \times 10^{11} \mathrm{Nm}^{-2}$ respectively)

1 $20 \mathrm{~Hz}$
2 $40 \mathrm{~Hz}$
3 $80 \mathrm{~Hz}$
4 $160 \mathrm{~Hz}$
Mechanical Properties of Solids

140965 One end of the steel rod is clamped to the stand and the other end is attached to a mass of 1000 $\mathrm{kg}$ as shown in the figure. The length of the rod is $50 \mathrm{~cm}$ and its cross-sectional area is 1000 $\mathrm{mm}^{2}$. The change in the length of the rod due to the weight of the mass is-
(Young's modulus of steel $=2 \times 10^{11} \mathrm{Nm}^{-2}$ and Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

1 $0.025 \mathrm{~mm}$
2 $0.10 \mathrm{~mm}$
3 $0.050 \mathrm{~mm}$
4 $0.075 \mathrm{~mm}$
Mechanical Properties of Solids

140966 A wire of length $L$ is hanging from a fixed supports. The length changes to $L_{1}$ and $L_{2}$ when masses $1 \mathrm{~kg}$ and $2 \mathrm{~kg}$ are suspended respectively from its free end. Then the value of $L$ is equal to

1 $\sqrt{\mathrm{L}_{1} \mathrm{~L}_{2}}$
2 $\frac{\mathrm{L}_{1}+\mathrm{L}_{2}}{2}$
3 $2 \mathrm{~L}_{1}-\mathrm{L}_{2}$
4 $3 \mathrm{~L}_{1}-2 \mathrm{~L}_{2}$
Mechanical Properties of Solids

140968 An object of mass $15 \mathrm{~kg}$ is attached to the end of a metal wire of unstretched length $1.0 \mathrm{~m}$. The object is then whirled in a vertical circle with an angular velocity of $4 \mathrm{rad} / \mathrm{s}$ at the bottom of the circle. If the cross sectional area of the wire is $0.05 \mathrm{~cm}^{2}$ and Young's modulus of metal is $2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$, then the elongation of the wire when the mass is at the lowest point of its path
(Take $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )

1 $0.27 \mathrm{~mm}$
2 $0.39 \mathrm{~mm}$
3 $0.55 \mathrm{~mm}$
4 $0.25 \mathrm{~mm}$
Mechanical Properties of Solids

140962 Two wires $A$ and $B$ of same cross-section are connected end to end. When same tension is created in both wires, the elongation in $B$ wire is twice the elongation in $A$ wire. If $L_{A}$ and $L_{B}$ are the initial lengths of the wires $A$ and $B$ respectively then (Young's modulus of material of wire $A=2 \times 10^{11} \mathrm{Nm}^{-2}$ and Young's modulus of material of wire $B=1.1 \times 10^{11} \mathrm{Nm}^{-2}$ )

1 $\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{10}{11}$
2 $\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{4}{5}$
3 $\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{9}{11}$
4 $\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{3}{7}$
Mechanical Properties of Solids

140964 A steel wire of length $1.25 \mathrm{~m}$ is stretched between two rigid supports. The tension in the wire produces an elastic strain of $0.14 \%$. The fundamental frequency of the wire is
(Density and Young's modules of steel are $7.7 \times$ $10^{3} \mathrm{kgm}^{-3}$ and $2.2 \times 10^{11} \mathrm{Nm}^{-2}$ respectively)

1 $20 \mathrm{~Hz}$
2 $40 \mathrm{~Hz}$
3 $80 \mathrm{~Hz}$
4 $160 \mathrm{~Hz}$
Mechanical Properties of Solids

140965 One end of the steel rod is clamped to the stand and the other end is attached to a mass of 1000 $\mathrm{kg}$ as shown in the figure. The length of the rod is $50 \mathrm{~cm}$ and its cross-sectional area is 1000 $\mathrm{mm}^{2}$. The change in the length of the rod due to the weight of the mass is-
(Young's modulus of steel $=2 \times 10^{11} \mathrm{Nm}^{-2}$ and Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

1 $0.025 \mathrm{~mm}$
2 $0.10 \mathrm{~mm}$
3 $0.050 \mathrm{~mm}$
4 $0.075 \mathrm{~mm}$
Mechanical Properties of Solids

140966 A wire of length $L$ is hanging from a fixed supports. The length changes to $L_{1}$ and $L_{2}$ when masses $1 \mathrm{~kg}$ and $2 \mathrm{~kg}$ are suspended respectively from its free end. Then the value of $L$ is equal to

1 $\sqrt{\mathrm{L}_{1} \mathrm{~L}_{2}}$
2 $\frac{\mathrm{L}_{1}+\mathrm{L}_{2}}{2}$
3 $2 \mathrm{~L}_{1}-\mathrm{L}_{2}$
4 $3 \mathrm{~L}_{1}-2 \mathrm{~L}_{2}$
Mechanical Properties of Solids

140968 An object of mass $15 \mathrm{~kg}$ is attached to the end of a metal wire of unstretched length $1.0 \mathrm{~m}$. The object is then whirled in a vertical circle with an angular velocity of $4 \mathrm{rad} / \mathrm{s}$ at the bottom of the circle. If the cross sectional area of the wire is $0.05 \mathrm{~cm}^{2}$ and Young's modulus of metal is $2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$, then the elongation of the wire when the mass is at the lowest point of its path
(Take $g=10 \mathrm{~m} / \mathrm{s}^{2}$ )

1 $0.27 \mathrm{~mm}$
2 $0.39 \mathrm{~mm}$
3 $0.55 \mathrm{~mm}$
4 $0.25 \mathrm{~mm}$