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

141039 A fluid of volume $1 \mathrm{~L}$ is subjected to a pressure change $1.0 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$. As a result its volume change by $0.4 \mathrm{~cm}^{3}$. The Bulk modulus of the fluid is

1 $2.5 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
2 $2.5 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$
3 $2.5 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$
4 $1.5 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$
Mechanical Properties of Solids

141040 Temperature of a gas is $20^{\circ} \mathrm{C}$ and pressure is changed from $1.01 \times 10^{5} \mathrm{~Pa}$ to $1.165 \times 10^{5} \mathrm{~Pa}$. If volume is decreased isothermally by $10 \%$. Bulk modulus of gas is

1 $1.55 \times 10^{5}$
2 $0.155 \times 10^{5}$
3 $1.4 \times 10^{5}$
4 $1.01 \times 10^{5}$
Mechanical Properties of Solids

141041 Young's modulus of rubber is $10^{4} \mathrm{~N} / \mathrm{m}^{2}$ and area of cross-section is $2 \mathrm{~cm}^{2}$. If force of $2 \times 10^{5}$ dyne is applied along its length, then its final length becomes

1 $3 \mathrm{~L}$
2 $4 \mathrm{~L}$
3 $2 \mathrm{~L}$
4 None of these
Mechanical Properties of Solids

141042 In the shown figure, length of the rod is $L$, area of cross-section A, Young's modulus of the material of the rod is $Y$. Then, $B$ and $A$ is subjected to a tensile force $F_{A}$ while force applied at end $B, F_{B}$ is lesser than $F_{A}$. Total change in length of the rod will be

1 $\mathrm{F}_{\mathrm{A}} \times \frac{\mathrm{L}}{2 \mathrm{AY}}$
2 $\mathrm{F}_{\mathrm{B}} \times \frac{\mathrm{L}}{2 \mathrm{AY}}$
3 $\frac{\left(\mathrm{F}_{\mathrm{A}}+\mathrm{F}_{\mathrm{B}}\right) \mathrm{L}}{2 \mathrm{AY}}$
4 $\frac{\left(\mathrm{F}_{\mathrm{A}}-\mathrm{F}_{\mathrm{B}}\right) \mathrm{L}}{2 \mathrm{AY}}$
Mechanical Properties of Solids

141043 Given $\sigma$ is the compressibility of water, $\rho$ is the density of water and $k$ is the bulk modulus of water. What is the energy density of water at the bottom of a lake $h$ meter deep?

1 $\frac{1}{2} \sigma(\mathrm{h} \rho \mathrm{g})^{2}$
2 $\frac{1}{2} \sigma(\mathrm{h} \rho \mathrm{g})$
3 $\frac{1}{2} \frac{\mathrm{h} \rho \mathrm{g}}{\sigma}$
4 $\frac{\mathrm{h} \rho g}{\sigma}$
Mechanical Properties of Solids

141039 A fluid of volume $1 \mathrm{~L}$ is subjected to a pressure change $1.0 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$. As a result its volume change by $0.4 \mathrm{~cm}^{3}$. The Bulk modulus of the fluid is

1 $2.5 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
2 $2.5 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$
3 $2.5 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$
4 $1.5 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$
Mechanical Properties of Solids

141040 Temperature of a gas is $20^{\circ} \mathrm{C}$ and pressure is changed from $1.01 \times 10^{5} \mathrm{~Pa}$ to $1.165 \times 10^{5} \mathrm{~Pa}$. If volume is decreased isothermally by $10 \%$. Bulk modulus of gas is

1 $1.55 \times 10^{5}$
2 $0.155 \times 10^{5}$
3 $1.4 \times 10^{5}$
4 $1.01 \times 10^{5}$
Mechanical Properties of Solids

141041 Young's modulus of rubber is $10^{4} \mathrm{~N} / \mathrm{m}^{2}$ and area of cross-section is $2 \mathrm{~cm}^{2}$. If force of $2 \times 10^{5}$ dyne is applied along its length, then its final length becomes

1 $3 \mathrm{~L}$
2 $4 \mathrm{~L}$
3 $2 \mathrm{~L}$
4 None of these
Mechanical Properties of Solids

141042 In the shown figure, length of the rod is $L$, area of cross-section A, Young's modulus of the material of the rod is $Y$. Then, $B$ and $A$ is subjected to a tensile force $F_{A}$ while force applied at end $B, F_{B}$ is lesser than $F_{A}$. Total change in length of the rod will be

1 $\mathrm{F}_{\mathrm{A}} \times \frac{\mathrm{L}}{2 \mathrm{AY}}$
2 $\mathrm{F}_{\mathrm{B}} \times \frac{\mathrm{L}}{2 \mathrm{AY}}$
3 $\frac{\left(\mathrm{F}_{\mathrm{A}}+\mathrm{F}_{\mathrm{B}}\right) \mathrm{L}}{2 \mathrm{AY}}$
4 $\frac{\left(\mathrm{F}_{\mathrm{A}}-\mathrm{F}_{\mathrm{B}}\right) \mathrm{L}}{2 \mathrm{AY}}$
Mechanical Properties of Solids

141043 Given $\sigma$ is the compressibility of water, $\rho$ is the density of water and $k$ is the bulk modulus of water. What is the energy density of water at the bottom of a lake $h$ meter deep?

1 $\frac{1}{2} \sigma(\mathrm{h} \rho \mathrm{g})^{2}$
2 $\frac{1}{2} \sigma(\mathrm{h} \rho \mathrm{g})$
3 $\frac{1}{2} \frac{\mathrm{h} \rho \mathrm{g}}{\sigma}$
4 $\frac{\mathrm{h} \rho g}{\sigma}$
Mechanical Properties of Solids

141039 A fluid of volume $1 \mathrm{~L}$ is subjected to a pressure change $1.0 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$. As a result its volume change by $0.4 \mathrm{~cm}^{3}$. The Bulk modulus of the fluid is

1 $2.5 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
2 $2.5 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$
3 $2.5 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$
4 $1.5 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$
Mechanical Properties of Solids

141040 Temperature of a gas is $20^{\circ} \mathrm{C}$ and pressure is changed from $1.01 \times 10^{5} \mathrm{~Pa}$ to $1.165 \times 10^{5} \mathrm{~Pa}$. If volume is decreased isothermally by $10 \%$. Bulk modulus of gas is

1 $1.55 \times 10^{5}$
2 $0.155 \times 10^{5}$
3 $1.4 \times 10^{5}$
4 $1.01 \times 10^{5}$
Mechanical Properties of Solids

141041 Young's modulus of rubber is $10^{4} \mathrm{~N} / \mathrm{m}^{2}$ and area of cross-section is $2 \mathrm{~cm}^{2}$. If force of $2 \times 10^{5}$ dyne is applied along its length, then its final length becomes

1 $3 \mathrm{~L}$
2 $4 \mathrm{~L}$
3 $2 \mathrm{~L}$
4 None of these
Mechanical Properties of Solids

141042 In the shown figure, length of the rod is $L$, area of cross-section A, Young's modulus of the material of the rod is $Y$. Then, $B$ and $A$ is subjected to a tensile force $F_{A}$ while force applied at end $B, F_{B}$ is lesser than $F_{A}$. Total change in length of the rod will be

1 $\mathrm{F}_{\mathrm{A}} \times \frac{\mathrm{L}}{2 \mathrm{AY}}$
2 $\mathrm{F}_{\mathrm{B}} \times \frac{\mathrm{L}}{2 \mathrm{AY}}$
3 $\frac{\left(\mathrm{F}_{\mathrm{A}}+\mathrm{F}_{\mathrm{B}}\right) \mathrm{L}}{2 \mathrm{AY}}$
4 $\frac{\left(\mathrm{F}_{\mathrm{A}}-\mathrm{F}_{\mathrm{B}}\right) \mathrm{L}}{2 \mathrm{AY}}$
Mechanical Properties of Solids

141043 Given $\sigma$ is the compressibility of water, $\rho$ is the density of water and $k$ is the bulk modulus of water. What is the energy density of water at the bottom of a lake $h$ meter deep?

1 $\frac{1}{2} \sigma(\mathrm{h} \rho \mathrm{g})^{2}$
2 $\frac{1}{2} \sigma(\mathrm{h} \rho \mathrm{g})$
3 $\frac{1}{2} \frac{\mathrm{h} \rho \mathrm{g}}{\sigma}$
4 $\frac{\mathrm{h} \rho g}{\sigma}$
Mechanical Properties of Solids

141039 A fluid of volume $1 \mathrm{~L}$ is subjected to a pressure change $1.0 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$. As a result its volume change by $0.4 \mathrm{~cm}^{3}$. The Bulk modulus of the fluid is

1 $2.5 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
2 $2.5 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$
3 $2.5 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$
4 $1.5 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$
Mechanical Properties of Solids

141040 Temperature of a gas is $20^{\circ} \mathrm{C}$ and pressure is changed from $1.01 \times 10^{5} \mathrm{~Pa}$ to $1.165 \times 10^{5} \mathrm{~Pa}$. If volume is decreased isothermally by $10 \%$. Bulk modulus of gas is

1 $1.55 \times 10^{5}$
2 $0.155 \times 10^{5}$
3 $1.4 \times 10^{5}$
4 $1.01 \times 10^{5}$
Mechanical Properties of Solids

141041 Young's modulus of rubber is $10^{4} \mathrm{~N} / \mathrm{m}^{2}$ and area of cross-section is $2 \mathrm{~cm}^{2}$. If force of $2 \times 10^{5}$ dyne is applied along its length, then its final length becomes

1 $3 \mathrm{~L}$
2 $4 \mathrm{~L}$
3 $2 \mathrm{~L}$
4 None of these
Mechanical Properties of Solids

141042 In the shown figure, length of the rod is $L$, area of cross-section A, Young's modulus of the material of the rod is $Y$. Then, $B$ and $A$ is subjected to a tensile force $F_{A}$ while force applied at end $B, F_{B}$ is lesser than $F_{A}$. Total change in length of the rod will be

1 $\mathrm{F}_{\mathrm{A}} \times \frac{\mathrm{L}}{2 \mathrm{AY}}$
2 $\mathrm{F}_{\mathrm{B}} \times \frac{\mathrm{L}}{2 \mathrm{AY}}$
3 $\frac{\left(\mathrm{F}_{\mathrm{A}}+\mathrm{F}_{\mathrm{B}}\right) \mathrm{L}}{2 \mathrm{AY}}$
4 $\frac{\left(\mathrm{F}_{\mathrm{A}}-\mathrm{F}_{\mathrm{B}}\right) \mathrm{L}}{2 \mathrm{AY}}$
Mechanical Properties of Solids

141043 Given $\sigma$ is the compressibility of water, $\rho$ is the density of water and $k$ is the bulk modulus of water. What is the energy density of water at the bottom of a lake $h$ meter deep?

1 $\frac{1}{2} \sigma(\mathrm{h} \rho \mathrm{g})^{2}$
2 $\frac{1}{2} \sigma(\mathrm{h} \rho \mathrm{g})$
3 $\frac{1}{2} \frac{\mathrm{h} \rho \mathrm{g}}{\sigma}$
4 $\frac{\mathrm{h} \rho g}{\sigma}$
Mechanical Properties of Solids

141039 A fluid of volume $1 \mathrm{~L}$ is subjected to a pressure change $1.0 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$. As a result its volume change by $0.4 \mathrm{~cm}^{3}$. The Bulk modulus of the fluid is

1 $2.5 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
2 $2.5 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$
3 $2.5 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$
4 $1.5 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$
Mechanical Properties of Solids

141040 Temperature of a gas is $20^{\circ} \mathrm{C}$ and pressure is changed from $1.01 \times 10^{5} \mathrm{~Pa}$ to $1.165 \times 10^{5} \mathrm{~Pa}$. If volume is decreased isothermally by $10 \%$. Bulk modulus of gas is

1 $1.55 \times 10^{5}$
2 $0.155 \times 10^{5}$
3 $1.4 \times 10^{5}$
4 $1.01 \times 10^{5}$
Mechanical Properties of Solids

141041 Young's modulus of rubber is $10^{4} \mathrm{~N} / \mathrm{m}^{2}$ and area of cross-section is $2 \mathrm{~cm}^{2}$. If force of $2 \times 10^{5}$ dyne is applied along its length, then its final length becomes

1 $3 \mathrm{~L}$
2 $4 \mathrm{~L}$
3 $2 \mathrm{~L}$
4 None of these
Mechanical Properties of Solids

141042 In the shown figure, length of the rod is $L$, area of cross-section A, Young's modulus of the material of the rod is $Y$. Then, $B$ and $A$ is subjected to a tensile force $F_{A}$ while force applied at end $B, F_{B}$ is lesser than $F_{A}$. Total change in length of the rod will be

1 $\mathrm{F}_{\mathrm{A}} \times \frac{\mathrm{L}}{2 \mathrm{AY}}$
2 $\mathrm{F}_{\mathrm{B}} \times \frac{\mathrm{L}}{2 \mathrm{AY}}$
3 $\frac{\left(\mathrm{F}_{\mathrm{A}}+\mathrm{F}_{\mathrm{B}}\right) \mathrm{L}}{2 \mathrm{AY}}$
4 $\frac{\left(\mathrm{F}_{\mathrm{A}}-\mathrm{F}_{\mathrm{B}}\right) \mathrm{L}}{2 \mathrm{AY}}$
Mechanical Properties of Solids

141043 Given $\sigma$ is the compressibility of water, $\rho$ is the density of water and $k$ is the bulk modulus of water. What is the energy density of water at the bottom of a lake $h$ meter deep?

1 $\frac{1}{2} \sigma(\mathrm{h} \rho \mathrm{g})^{2}$
2 $\frac{1}{2} \sigma(\mathrm{h} \rho \mathrm{g})$
3 $\frac{1}{2} \frac{\mathrm{h} \rho \mathrm{g}}{\sigma}$
4 $\frac{\mathrm{h} \rho g}{\sigma}$