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

140992 What should be the diameter of a copper wire $\left(Y=12 \times 10^{10} \mathrm{Nm}^{-2}\right)$ of length $5 \mathrm{~m}$ to produce the same elongation produced by a $5 \mathrm{~m}$ long aluminum wire $\left(Y=7 \times 10^{10} \mathrm{Nm}^{-2}\right)$ of diameter $3 \mathrm{~mm}$ with the same $40 \mathrm{~kg}$ mass?

1 $1.5 \mathrm{~mm}$
2 $5 \mathrm{~mm}$
3 $2.3 \mathrm{~mm}$
4 $10 \mathrm{~mm}$
Mechanical Properties of Solids

140993 If a pressure of $8 \times 10^{8} \mathrm{~N} \mathrm{~m}^{-2}$ is applied to a lead block, so that its volume reduces by $20 \%$. The Bulk modulus of lead block is

1 $4 \times 10^{7} \mathrm{Nm}^{-2}$
2 $4 \times 10^{8} \mathrm{Nm}^{-2}$
3 $4 \times 10^{9} \mathrm{Nm}^{-2}$
4 $4 \times 10^{10} \mathrm{Nm}^{-2}$
Mechanical Properties of Solids

140994 When a weight of $10 \mathrm{~kg}$ is suspended from a copper wire of length $3 \mathrm{~m}$ and diameter $0.4 \mathrm{~mm}$, its length increases by $2.4 \mathrm{~cm}$. If the diameter of the wire is doubled, then the extension in its length will be

1 $9.6 \mathrm{~cm}$
2 $4.8 \mathrm{~cm}$
3 $1.2 \mathrm{~cm}$
4 $0.6 \mathrm{~cm}$
Mechanical Properties of Solids

140997 A metal sphere of radius $1 \mathrm{~m}$ is charged with $10^{-2} \mathrm{C}$ in air. Its bulk modulus is $10^{11} / 4 \pi^{2} \mathrm{~N} / \mathrm{m}^{2}$. The volume strain in the sphere is
( $\varepsilon_{0}=$ permittivity of free space)

1 $\frac{10^{-14}}{8 \varepsilon_{0}}$
2 $\frac{10^{-12}}{4 \varepsilon_{0}}$
3 $\frac{10^{-15}}{8 \varepsilon_{0}}$
4 $\frac{10^{-1}}{6 \varepsilon_{0}}$
Mechanical Properties of Solids

140992 What should be the diameter of a copper wire $\left(Y=12 \times 10^{10} \mathrm{Nm}^{-2}\right)$ of length $5 \mathrm{~m}$ to produce the same elongation produced by a $5 \mathrm{~m}$ long aluminum wire $\left(Y=7 \times 10^{10} \mathrm{Nm}^{-2}\right)$ of diameter $3 \mathrm{~mm}$ with the same $40 \mathrm{~kg}$ mass?

1 $1.5 \mathrm{~mm}$
2 $5 \mathrm{~mm}$
3 $2.3 \mathrm{~mm}$
4 $10 \mathrm{~mm}$
Mechanical Properties of Solids

140993 If a pressure of $8 \times 10^{8} \mathrm{~N} \mathrm{~m}^{-2}$ is applied to a lead block, so that its volume reduces by $20 \%$. The Bulk modulus of lead block is

1 $4 \times 10^{7} \mathrm{Nm}^{-2}$
2 $4 \times 10^{8} \mathrm{Nm}^{-2}$
3 $4 \times 10^{9} \mathrm{Nm}^{-2}$
4 $4 \times 10^{10} \mathrm{Nm}^{-2}$
Mechanical Properties of Solids

140994 When a weight of $10 \mathrm{~kg}$ is suspended from a copper wire of length $3 \mathrm{~m}$ and diameter $0.4 \mathrm{~mm}$, its length increases by $2.4 \mathrm{~cm}$. If the diameter of the wire is doubled, then the extension in its length will be

1 $9.6 \mathrm{~cm}$
2 $4.8 \mathrm{~cm}$
3 $1.2 \mathrm{~cm}$
4 $0.6 \mathrm{~cm}$
Mechanical Properties of Solids

140997 A metal sphere of radius $1 \mathrm{~m}$ is charged with $10^{-2} \mathrm{C}$ in air. Its bulk modulus is $10^{11} / 4 \pi^{2} \mathrm{~N} / \mathrm{m}^{2}$. The volume strain in the sphere is
( $\varepsilon_{0}=$ permittivity of free space)

1 $\frac{10^{-14}}{8 \varepsilon_{0}}$
2 $\frac{10^{-12}}{4 \varepsilon_{0}}$
3 $\frac{10^{-15}}{8 \varepsilon_{0}}$
4 $\frac{10^{-1}}{6 \varepsilon_{0}}$
Mechanical Properties of Solids

140992 What should be the diameter of a copper wire $\left(Y=12 \times 10^{10} \mathrm{Nm}^{-2}\right)$ of length $5 \mathrm{~m}$ to produce the same elongation produced by a $5 \mathrm{~m}$ long aluminum wire $\left(Y=7 \times 10^{10} \mathrm{Nm}^{-2}\right)$ of diameter $3 \mathrm{~mm}$ with the same $40 \mathrm{~kg}$ mass?

1 $1.5 \mathrm{~mm}$
2 $5 \mathrm{~mm}$
3 $2.3 \mathrm{~mm}$
4 $10 \mathrm{~mm}$
Mechanical Properties of Solids

140993 If a pressure of $8 \times 10^{8} \mathrm{~N} \mathrm{~m}^{-2}$ is applied to a lead block, so that its volume reduces by $20 \%$. The Bulk modulus of lead block is

1 $4 \times 10^{7} \mathrm{Nm}^{-2}$
2 $4 \times 10^{8} \mathrm{Nm}^{-2}$
3 $4 \times 10^{9} \mathrm{Nm}^{-2}$
4 $4 \times 10^{10} \mathrm{Nm}^{-2}$
Mechanical Properties of Solids

140994 When a weight of $10 \mathrm{~kg}$ is suspended from a copper wire of length $3 \mathrm{~m}$ and diameter $0.4 \mathrm{~mm}$, its length increases by $2.4 \mathrm{~cm}$. If the diameter of the wire is doubled, then the extension in its length will be

1 $9.6 \mathrm{~cm}$
2 $4.8 \mathrm{~cm}$
3 $1.2 \mathrm{~cm}$
4 $0.6 \mathrm{~cm}$
Mechanical Properties of Solids

140997 A metal sphere of radius $1 \mathrm{~m}$ is charged with $10^{-2} \mathrm{C}$ in air. Its bulk modulus is $10^{11} / 4 \pi^{2} \mathrm{~N} / \mathrm{m}^{2}$. The volume strain in the sphere is
( $\varepsilon_{0}=$ permittivity of free space)

1 $\frac{10^{-14}}{8 \varepsilon_{0}}$
2 $\frac{10^{-12}}{4 \varepsilon_{0}}$
3 $\frac{10^{-15}}{8 \varepsilon_{0}}$
4 $\frac{10^{-1}}{6 \varepsilon_{0}}$
Mechanical Properties of Solids

140992 What should be the diameter of a copper wire $\left(Y=12 \times 10^{10} \mathrm{Nm}^{-2}\right)$ of length $5 \mathrm{~m}$ to produce the same elongation produced by a $5 \mathrm{~m}$ long aluminum wire $\left(Y=7 \times 10^{10} \mathrm{Nm}^{-2}\right)$ of diameter $3 \mathrm{~mm}$ with the same $40 \mathrm{~kg}$ mass?

1 $1.5 \mathrm{~mm}$
2 $5 \mathrm{~mm}$
3 $2.3 \mathrm{~mm}$
4 $10 \mathrm{~mm}$
Mechanical Properties of Solids

140993 If a pressure of $8 \times 10^{8} \mathrm{~N} \mathrm{~m}^{-2}$ is applied to a lead block, so that its volume reduces by $20 \%$. The Bulk modulus of lead block is

1 $4 \times 10^{7} \mathrm{Nm}^{-2}$
2 $4 \times 10^{8} \mathrm{Nm}^{-2}$
3 $4 \times 10^{9} \mathrm{Nm}^{-2}$
4 $4 \times 10^{10} \mathrm{Nm}^{-2}$
Mechanical Properties of Solids

140994 When a weight of $10 \mathrm{~kg}$ is suspended from a copper wire of length $3 \mathrm{~m}$ and diameter $0.4 \mathrm{~mm}$, its length increases by $2.4 \mathrm{~cm}$. If the diameter of the wire is doubled, then the extension in its length will be

1 $9.6 \mathrm{~cm}$
2 $4.8 \mathrm{~cm}$
3 $1.2 \mathrm{~cm}$
4 $0.6 \mathrm{~cm}$
Mechanical Properties of Solids

140997 A metal sphere of radius $1 \mathrm{~m}$ is charged with $10^{-2} \mathrm{C}$ in air. Its bulk modulus is $10^{11} / 4 \pi^{2} \mathrm{~N} / \mathrm{m}^{2}$. The volume strain in the sphere is
( $\varepsilon_{0}=$ permittivity of free space)

1 $\frac{10^{-14}}{8 \varepsilon_{0}}$
2 $\frac{10^{-12}}{4 \varepsilon_{0}}$
3 $\frac{10^{-15}}{8 \varepsilon_{0}}$
4 $\frac{10^{-1}}{6 \varepsilon_{0}}$