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

140980 The bulk modulus of a spherical object is "B". If it is subjected to uniform pressure ' $p$ ', the fractional decrease in radius is

1 $\frac{B}{3 p}$
2 $\frac{3 p}{B}$
3 $\frac{\mathrm{p}}{3 \mathrm{~B}}$
4 $\frac{p}{B}$
Mechanical Properties of Solids

140981 Consider a rod of length $1.0 \mathrm{~m}$ with a crosssectional area of $0.50 \mathrm{~cm}^{2}$. The rod supports a 500-kg platform that hangs attached to the rod's lower end. What is elongation of the rod under the stress ignoring the weight of the rod? Consider the Young's modulus to be $10^{11} \mathrm{~Pa}$ and $g=10 \mathrm{~m} / \mathrm{s}^{2}$

1 $2 \mathrm{~mm}$
2 $0.5 \mathrm{~mm}$
3 $1.5 \mathrm{~mm}$
4 $1 \mathrm{~mm}$
Mechanical Properties of Solids

140983 The Young's modulus of a rubber string of length $12 \mathrm{~cm}$ and density $1.5 \mathrm{kgm}^{-3}$ is $5 \times 10^{8} \mathrm{~N}$. $\mathrm{m}^{-2}$. When this string is suspended vertically, the increase in its length due to its own weight is ___ (take $\mathrm{g}=10 \mathrm{~m} . \mathrm{s}^{-2}$ )

1 $2.16 \times 10^{-10} \mathrm{~m}$
2 $9.6 \times 10^{-11} \mathrm{~m}$
3 $9.6 \times 10^{-3} \mathrm{~m}$
4 $2.16 \times 10^{-3} \mathrm{~m}$
Mechanical Properties of Solids

140985 A wire of length $L$, area of cross-section $A$ is hanging from a fixed support. The length of the wire changes to $L_{1}$ when mass $M$ is suspended from its free end. The expression for Young's modulus is

1 $\frac{\operatorname{Mg}\left(\mathrm{L}_{1}-\mathrm{L}\right)}{\mathrm{AL}}$
2 $\frac{\mathrm{MgL}}{\mathrm{AL}_{1}}$
3 $\frac{\mathrm{MgL}}{\mathrm{A}\left(\mathrm{L}_{1}-\mathrm{L}\right)}$
4 $\frac{\mathrm{MgL}}{\mathrm{AL}}$
Mechanical Properties of Solids

140980 The bulk modulus of a spherical object is "B". If it is subjected to uniform pressure ' $p$ ', the fractional decrease in radius is

1 $\frac{B}{3 p}$
2 $\frac{3 p}{B}$
3 $\frac{\mathrm{p}}{3 \mathrm{~B}}$
4 $\frac{p}{B}$
Mechanical Properties of Solids

140981 Consider a rod of length $1.0 \mathrm{~m}$ with a crosssectional area of $0.50 \mathrm{~cm}^{2}$. The rod supports a 500-kg platform that hangs attached to the rod's lower end. What is elongation of the rod under the stress ignoring the weight of the rod? Consider the Young's modulus to be $10^{11} \mathrm{~Pa}$ and $g=10 \mathrm{~m} / \mathrm{s}^{2}$

1 $2 \mathrm{~mm}$
2 $0.5 \mathrm{~mm}$
3 $1.5 \mathrm{~mm}$
4 $1 \mathrm{~mm}$
Mechanical Properties of Solids

140983 The Young's modulus of a rubber string of length $12 \mathrm{~cm}$ and density $1.5 \mathrm{kgm}^{-3}$ is $5 \times 10^{8} \mathrm{~N}$. $\mathrm{m}^{-2}$. When this string is suspended vertically, the increase in its length due to its own weight is ___ (take $\mathrm{g}=10 \mathrm{~m} . \mathrm{s}^{-2}$ )

1 $2.16 \times 10^{-10} \mathrm{~m}$
2 $9.6 \times 10^{-11} \mathrm{~m}$
3 $9.6 \times 10^{-3} \mathrm{~m}$
4 $2.16 \times 10^{-3} \mathrm{~m}$
Mechanical Properties of Solids

140985 A wire of length $L$, area of cross-section $A$ is hanging from a fixed support. The length of the wire changes to $L_{1}$ when mass $M$ is suspended from its free end. The expression for Young's modulus is

1 $\frac{\operatorname{Mg}\left(\mathrm{L}_{1}-\mathrm{L}\right)}{\mathrm{AL}}$
2 $\frac{\mathrm{MgL}}{\mathrm{AL}_{1}}$
3 $\frac{\mathrm{MgL}}{\mathrm{A}\left(\mathrm{L}_{1}-\mathrm{L}\right)}$
4 $\frac{\mathrm{MgL}}{\mathrm{AL}}$
Mechanical Properties of Solids

140980 The bulk modulus of a spherical object is "B". If it is subjected to uniform pressure ' $p$ ', the fractional decrease in radius is

1 $\frac{B}{3 p}$
2 $\frac{3 p}{B}$
3 $\frac{\mathrm{p}}{3 \mathrm{~B}}$
4 $\frac{p}{B}$
Mechanical Properties of Solids

140981 Consider a rod of length $1.0 \mathrm{~m}$ with a crosssectional area of $0.50 \mathrm{~cm}^{2}$. The rod supports a 500-kg platform that hangs attached to the rod's lower end. What is elongation of the rod under the stress ignoring the weight of the rod? Consider the Young's modulus to be $10^{11} \mathrm{~Pa}$ and $g=10 \mathrm{~m} / \mathrm{s}^{2}$

1 $2 \mathrm{~mm}$
2 $0.5 \mathrm{~mm}$
3 $1.5 \mathrm{~mm}$
4 $1 \mathrm{~mm}$
Mechanical Properties of Solids

140983 The Young's modulus of a rubber string of length $12 \mathrm{~cm}$ and density $1.5 \mathrm{kgm}^{-3}$ is $5 \times 10^{8} \mathrm{~N}$. $\mathrm{m}^{-2}$. When this string is suspended vertically, the increase in its length due to its own weight is ___ (take $\mathrm{g}=10 \mathrm{~m} . \mathrm{s}^{-2}$ )

1 $2.16 \times 10^{-10} \mathrm{~m}$
2 $9.6 \times 10^{-11} \mathrm{~m}$
3 $9.6 \times 10^{-3} \mathrm{~m}$
4 $2.16 \times 10^{-3} \mathrm{~m}$
Mechanical Properties of Solids

140985 A wire of length $L$, area of cross-section $A$ is hanging from a fixed support. The length of the wire changes to $L_{1}$ when mass $M$ is suspended from its free end. The expression for Young's modulus is

1 $\frac{\operatorname{Mg}\left(\mathrm{L}_{1}-\mathrm{L}\right)}{\mathrm{AL}}$
2 $\frac{\mathrm{MgL}}{\mathrm{AL}_{1}}$
3 $\frac{\mathrm{MgL}}{\mathrm{A}\left(\mathrm{L}_{1}-\mathrm{L}\right)}$
4 $\frac{\mathrm{MgL}}{\mathrm{AL}}$
Mechanical Properties of Solids

140980 The bulk modulus of a spherical object is "B". If it is subjected to uniform pressure ' $p$ ', the fractional decrease in radius is

1 $\frac{B}{3 p}$
2 $\frac{3 p}{B}$
3 $\frac{\mathrm{p}}{3 \mathrm{~B}}$
4 $\frac{p}{B}$
Mechanical Properties of Solids

140981 Consider a rod of length $1.0 \mathrm{~m}$ with a crosssectional area of $0.50 \mathrm{~cm}^{2}$. The rod supports a 500-kg platform that hangs attached to the rod's lower end. What is elongation of the rod under the stress ignoring the weight of the rod? Consider the Young's modulus to be $10^{11} \mathrm{~Pa}$ and $g=10 \mathrm{~m} / \mathrm{s}^{2}$

1 $2 \mathrm{~mm}$
2 $0.5 \mathrm{~mm}$
3 $1.5 \mathrm{~mm}$
4 $1 \mathrm{~mm}$
Mechanical Properties of Solids

140983 The Young's modulus of a rubber string of length $12 \mathrm{~cm}$ and density $1.5 \mathrm{kgm}^{-3}$ is $5 \times 10^{8} \mathrm{~N}$. $\mathrm{m}^{-2}$. When this string is suspended vertically, the increase in its length due to its own weight is ___ (take $\mathrm{g}=10 \mathrm{~m} . \mathrm{s}^{-2}$ )

1 $2.16 \times 10^{-10} \mathrm{~m}$
2 $9.6 \times 10^{-11} \mathrm{~m}$
3 $9.6 \times 10^{-3} \mathrm{~m}$
4 $2.16 \times 10^{-3} \mathrm{~m}$
Mechanical Properties of Solids

140985 A wire of length $L$, area of cross-section $A$ is hanging from a fixed support. The length of the wire changes to $L_{1}$ when mass $M$ is suspended from its free end. The expression for Young's modulus is

1 $\frac{\operatorname{Mg}\left(\mathrm{L}_{1}-\mathrm{L}\right)}{\mathrm{AL}}$
2 $\frac{\mathrm{MgL}}{\mathrm{AL}_{1}}$
3 $\frac{\mathrm{MgL}}{\mathrm{A}\left(\mathrm{L}_{1}-\mathrm{L}\right)}$
4 $\frac{\mathrm{MgL}}{\mathrm{AL}}$