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

140948 A $100 \mathrm{~m}$ long wire having cross-sectional area $6.25 \times 10^{-4} \mathrm{~m}^{2}$ and Young's modulus is $10^{10}$ $\mathrm{Nm}^{-2}$ is subjected to a load of $250 \mathrm{~N}$, then the elongation in the wire will be:

1 $6.25 \times 10^{-3} \mathrm{~m}$
2 $4 \times 10^{-3} \mathrm{~m}$
3 $4 \times 10^{-4} \mathrm{~m}$
4 $6.25 \times 10^{-6} \mathrm{~m}$
Mechanical Properties of Solids

140949 For a solid rod, the young's modulus of elasticity is $3.2 \times 10^{11} \mathrm{Nm}^{-2}$ and density is $8 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$ the velocity of longitudinal wave in the rod will be.

1 $3.65 \times 10^{3} \mathrm{~ms}^{-1}$
2 $18.96 \times 10^{3} \mathrm{~ms}^{-1}$
3 $145.75 \times 10^{3} \mathrm{~ms}^{-1}$
4 $6.32 \times 10^{3} \mathrm{~m} \mathrm{~s}^{-1}$
Mechanical Properties of Solids

140950 Under the same load, wire $A$ having length $5.0 \mathrm{~m}$ and cross section $2.5 \times 10^{-5} \mathrm{~m}^{2}$ stretches uniformly by the same amount as another wire $B$ of length $6.0 \mathrm{~m}$ and across section of $3.0 \times 10^{-5}$ $\mathrm{m}^{2}$ stretches. The ratio of the Young's modulus of wire $A$ to that wire $B$ will be:

1 $1: 4$
2 $1: 1$
3 $1: 10$
4 $1: 2$
Mechanical Properties of Solids

140951 The dimensions of four wires of the same material are given below. In which wire the increase in length will be maximum when the same tension is applied?

1 Length $100 \mathrm{~cm}$, diameter $1 \mathrm{~mm}$
2 Length $200 \mathrm{~cm}$, diameter $2 \mathrm{~mm}$
3 Length $300 \mathrm{~cm}$, diameter $3 \mathrm{~mm}$
4 Length $50 \mathrm{~cm}$, diameter $0.5 \mathrm{~mm}$
Mechanical Properties of Solids

140953 A swimming pool has a depth of $22 \mathrm{~m}$ and area of $700 \mathrm{~m}^{2}$. Calculate fractional change $\frac{\Delta V}{V}$ of water at the bottom of the swimming pool. Given that the bulk modulus of water is $2.2 \times 10^{9} \mathrm{Nm}^{-2}, \mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^{2}$ and density of water is $1000 \mathrm{~kg} / \mathrm{m}^{3}$

1 $2.2 \times 10^{-4}$
2 $0.7 \times 10^{-4}$
3 $0.31 \times 10^{-4}$
4 $10^{-4}$
Mechanical Properties of Solids

140948 A $100 \mathrm{~m}$ long wire having cross-sectional area $6.25 \times 10^{-4} \mathrm{~m}^{2}$ and Young's modulus is $10^{10}$ $\mathrm{Nm}^{-2}$ is subjected to a load of $250 \mathrm{~N}$, then the elongation in the wire will be:

1 $6.25 \times 10^{-3} \mathrm{~m}$
2 $4 \times 10^{-3} \mathrm{~m}$
3 $4 \times 10^{-4} \mathrm{~m}$
4 $6.25 \times 10^{-6} \mathrm{~m}$
Mechanical Properties of Solids

140949 For a solid rod, the young's modulus of elasticity is $3.2 \times 10^{11} \mathrm{Nm}^{-2}$ and density is $8 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$ the velocity of longitudinal wave in the rod will be.

1 $3.65 \times 10^{3} \mathrm{~ms}^{-1}$
2 $18.96 \times 10^{3} \mathrm{~ms}^{-1}$
3 $145.75 \times 10^{3} \mathrm{~ms}^{-1}$
4 $6.32 \times 10^{3} \mathrm{~m} \mathrm{~s}^{-1}$
Mechanical Properties of Solids

140950 Under the same load, wire $A$ having length $5.0 \mathrm{~m}$ and cross section $2.5 \times 10^{-5} \mathrm{~m}^{2}$ stretches uniformly by the same amount as another wire $B$ of length $6.0 \mathrm{~m}$ and across section of $3.0 \times 10^{-5}$ $\mathrm{m}^{2}$ stretches. The ratio of the Young's modulus of wire $A$ to that wire $B$ will be:

1 $1: 4$
2 $1: 1$
3 $1: 10$
4 $1: 2$
Mechanical Properties of Solids

140951 The dimensions of four wires of the same material are given below. In which wire the increase in length will be maximum when the same tension is applied?

1 Length $100 \mathrm{~cm}$, diameter $1 \mathrm{~mm}$
2 Length $200 \mathrm{~cm}$, diameter $2 \mathrm{~mm}$
3 Length $300 \mathrm{~cm}$, diameter $3 \mathrm{~mm}$
4 Length $50 \mathrm{~cm}$, diameter $0.5 \mathrm{~mm}$
Mechanical Properties of Solids

140953 A swimming pool has a depth of $22 \mathrm{~m}$ and area of $700 \mathrm{~m}^{2}$. Calculate fractional change $\frac{\Delta V}{V}$ of water at the bottom of the swimming pool. Given that the bulk modulus of water is $2.2 \times 10^{9} \mathrm{Nm}^{-2}, \mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^{2}$ and density of water is $1000 \mathrm{~kg} / \mathrm{m}^{3}$

1 $2.2 \times 10^{-4}$
2 $0.7 \times 10^{-4}$
3 $0.31 \times 10^{-4}$
4 $10^{-4}$
Mechanical Properties of Solids

140948 A $100 \mathrm{~m}$ long wire having cross-sectional area $6.25 \times 10^{-4} \mathrm{~m}^{2}$ and Young's modulus is $10^{10}$ $\mathrm{Nm}^{-2}$ is subjected to a load of $250 \mathrm{~N}$, then the elongation in the wire will be:

1 $6.25 \times 10^{-3} \mathrm{~m}$
2 $4 \times 10^{-3} \mathrm{~m}$
3 $4 \times 10^{-4} \mathrm{~m}$
4 $6.25 \times 10^{-6} \mathrm{~m}$
Mechanical Properties of Solids

140949 For a solid rod, the young's modulus of elasticity is $3.2 \times 10^{11} \mathrm{Nm}^{-2}$ and density is $8 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$ the velocity of longitudinal wave in the rod will be.

1 $3.65 \times 10^{3} \mathrm{~ms}^{-1}$
2 $18.96 \times 10^{3} \mathrm{~ms}^{-1}$
3 $145.75 \times 10^{3} \mathrm{~ms}^{-1}$
4 $6.32 \times 10^{3} \mathrm{~m} \mathrm{~s}^{-1}$
Mechanical Properties of Solids

140950 Under the same load, wire $A$ having length $5.0 \mathrm{~m}$ and cross section $2.5 \times 10^{-5} \mathrm{~m}^{2}$ stretches uniformly by the same amount as another wire $B$ of length $6.0 \mathrm{~m}$ and across section of $3.0 \times 10^{-5}$ $\mathrm{m}^{2}$ stretches. The ratio of the Young's modulus of wire $A$ to that wire $B$ will be:

1 $1: 4$
2 $1: 1$
3 $1: 10$
4 $1: 2$
Mechanical Properties of Solids

140951 The dimensions of four wires of the same material are given below. In which wire the increase in length will be maximum when the same tension is applied?

1 Length $100 \mathrm{~cm}$, diameter $1 \mathrm{~mm}$
2 Length $200 \mathrm{~cm}$, diameter $2 \mathrm{~mm}$
3 Length $300 \mathrm{~cm}$, diameter $3 \mathrm{~mm}$
4 Length $50 \mathrm{~cm}$, diameter $0.5 \mathrm{~mm}$
Mechanical Properties of Solids

140953 A swimming pool has a depth of $22 \mathrm{~m}$ and area of $700 \mathrm{~m}^{2}$. Calculate fractional change $\frac{\Delta V}{V}$ of water at the bottom of the swimming pool. Given that the bulk modulus of water is $2.2 \times 10^{9} \mathrm{Nm}^{-2}, \mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^{2}$ and density of water is $1000 \mathrm{~kg} / \mathrm{m}^{3}$

1 $2.2 \times 10^{-4}$
2 $0.7 \times 10^{-4}$
3 $0.31 \times 10^{-4}$
4 $10^{-4}$
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Mechanical Properties of Solids

140948 A $100 \mathrm{~m}$ long wire having cross-sectional area $6.25 \times 10^{-4} \mathrm{~m}^{2}$ and Young's modulus is $10^{10}$ $\mathrm{Nm}^{-2}$ is subjected to a load of $250 \mathrm{~N}$, then the elongation in the wire will be:

1 $6.25 \times 10^{-3} \mathrm{~m}$
2 $4 \times 10^{-3} \mathrm{~m}$
3 $4 \times 10^{-4} \mathrm{~m}$
4 $6.25 \times 10^{-6} \mathrm{~m}$
Mechanical Properties of Solids

140949 For a solid rod, the young's modulus of elasticity is $3.2 \times 10^{11} \mathrm{Nm}^{-2}$ and density is $8 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$ the velocity of longitudinal wave in the rod will be.

1 $3.65 \times 10^{3} \mathrm{~ms}^{-1}$
2 $18.96 \times 10^{3} \mathrm{~ms}^{-1}$
3 $145.75 \times 10^{3} \mathrm{~ms}^{-1}$
4 $6.32 \times 10^{3} \mathrm{~m} \mathrm{~s}^{-1}$
Mechanical Properties of Solids

140950 Under the same load, wire $A$ having length $5.0 \mathrm{~m}$ and cross section $2.5 \times 10^{-5} \mathrm{~m}^{2}$ stretches uniformly by the same amount as another wire $B$ of length $6.0 \mathrm{~m}$ and across section of $3.0 \times 10^{-5}$ $\mathrm{m}^{2}$ stretches. The ratio of the Young's modulus of wire $A$ to that wire $B$ will be:

1 $1: 4$
2 $1: 1$
3 $1: 10$
4 $1: 2$
Mechanical Properties of Solids

140951 The dimensions of four wires of the same material are given below. In which wire the increase in length will be maximum when the same tension is applied?

1 Length $100 \mathrm{~cm}$, diameter $1 \mathrm{~mm}$
2 Length $200 \mathrm{~cm}$, diameter $2 \mathrm{~mm}$
3 Length $300 \mathrm{~cm}$, diameter $3 \mathrm{~mm}$
4 Length $50 \mathrm{~cm}$, diameter $0.5 \mathrm{~mm}$
Mechanical Properties of Solids

140953 A swimming pool has a depth of $22 \mathrm{~m}$ and area of $700 \mathrm{~m}^{2}$. Calculate fractional change $\frac{\Delta V}{V}$ of water at the bottom of the swimming pool. Given that the bulk modulus of water is $2.2 \times 10^{9} \mathrm{Nm}^{-2}, \mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^{2}$ and density of water is $1000 \mathrm{~kg} / \mathrm{m}^{3}$

1 $2.2 \times 10^{-4}$
2 $0.7 \times 10^{-4}$
3 $0.31 \times 10^{-4}$
4 $10^{-4}$
Mechanical Properties of Solids

140948 A $100 \mathrm{~m}$ long wire having cross-sectional area $6.25 \times 10^{-4} \mathrm{~m}^{2}$ and Young's modulus is $10^{10}$ $\mathrm{Nm}^{-2}$ is subjected to a load of $250 \mathrm{~N}$, then the elongation in the wire will be:

1 $6.25 \times 10^{-3} \mathrm{~m}$
2 $4 \times 10^{-3} \mathrm{~m}$
3 $4 \times 10^{-4} \mathrm{~m}$
4 $6.25 \times 10^{-6} \mathrm{~m}$
Mechanical Properties of Solids

140949 For a solid rod, the young's modulus of elasticity is $3.2 \times 10^{11} \mathrm{Nm}^{-2}$ and density is $8 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$ the velocity of longitudinal wave in the rod will be.

1 $3.65 \times 10^{3} \mathrm{~ms}^{-1}$
2 $18.96 \times 10^{3} \mathrm{~ms}^{-1}$
3 $145.75 \times 10^{3} \mathrm{~ms}^{-1}$
4 $6.32 \times 10^{3} \mathrm{~m} \mathrm{~s}^{-1}$
Mechanical Properties of Solids

140950 Under the same load, wire $A$ having length $5.0 \mathrm{~m}$ and cross section $2.5 \times 10^{-5} \mathrm{~m}^{2}$ stretches uniformly by the same amount as another wire $B$ of length $6.0 \mathrm{~m}$ and across section of $3.0 \times 10^{-5}$ $\mathrm{m}^{2}$ stretches. The ratio of the Young's modulus of wire $A$ to that wire $B$ will be:

1 $1: 4$
2 $1: 1$
3 $1: 10$
4 $1: 2$
Mechanical Properties of Solids

140951 The dimensions of four wires of the same material are given below. In which wire the increase in length will be maximum when the same tension is applied?

1 Length $100 \mathrm{~cm}$, diameter $1 \mathrm{~mm}$
2 Length $200 \mathrm{~cm}$, diameter $2 \mathrm{~mm}$
3 Length $300 \mathrm{~cm}$, diameter $3 \mathrm{~mm}$
4 Length $50 \mathrm{~cm}$, diameter $0.5 \mathrm{~mm}$
Mechanical Properties of Solids

140953 A swimming pool has a depth of $22 \mathrm{~m}$ and area of $700 \mathrm{~m}^{2}$. Calculate fractional change $\frac{\Delta V}{V}$ of water at the bottom of the swimming pool. Given that the bulk modulus of water is $2.2 \times 10^{9} \mathrm{Nm}^{-2}, \mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^{2}$ and density of water is $1000 \mathrm{~kg} / \mathrm{m}^{3}$

1 $2.2 \times 10^{-4}$
2 $0.7 \times 10^{-4}$
3 $0.31 \times 10^{-4}$
4 $10^{-4}$