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

141012 For a material the ratio of Young's modulus to rigidity modulus is 2.8 . If some force is applied on a wire made of this material. Its crosssectional area decreases by $2 \%$. The percentage change in its length is

1 0.4
2 1.6
3 2.5
4 4
Mechanical Properties of Solids

141014 A rubber cord of density d, Young's modulus $Y$ and length $L$ is suspended vertically. If the cord extends by a length $0.5 \mathrm{~L}$ under its own weight, then $L$ is

1 $\frac{Y}{2 d g}$
2 $\frac{Y}{\mathrm{dg}}$
3 $\frac{2 \mathrm{Y}}{\mathrm{dg}}$
4 $\frac{\mathrm{dg}}{2 \mathrm{Y}}$
5 $\frac{\mathrm{dg}}{\mathrm{Y}}$
Mechanical Properties of Solids

141015 One end of a long metallic wire of length $L$, area of cross-section $A$ and Young's modulus $Y$ is tied to the ceiling. The other end is tied to a massless spring of force constant $k$ and mass $m$ is hung from the free end of the spring. If $m$ is slightly pulled down and released, then its time period of oscillation is

1 $2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$
2 $2 \pi \sqrt{\frac{\mathrm{mYA}}{\mathrm{kL}}}$
3 $2 \pi \sqrt{\frac{\mathrm{m}(\mathrm{kA}+\mathrm{YL})}{\mathrm{kYA}}}$
4 $2 \pi \sqrt{\frac{\mathrm{m}(\mathrm{kL}+\mathrm{YA})}{\mathrm{kYA}}}$
Mechanical Properties of Solids

141017 In a tensile test on a metal bar of diameter $0.015 \mathrm{~m}$ and length $0.2 \mathrm{~m}$, the relation between the load and elongation within the proportional limit is found to be $F=97.2 \times 10^{6}(\Delta L)$, where $F$ is the load (in $N$ ) and $\Delta L$ is the elongation (in $m)$. The Young's modulus of the material in GPa is

1 75.5
2 85.6
3 98.7
4 110
Mechanical Properties of Solids

141012 For a material the ratio of Young's modulus to rigidity modulus is 2.8 . If some force is applied on a wire made of this material. Its crosssectional area decreases by $2 \%$. The percentage change in its length is

1 0.4
2 1.6
3 2.5
4 4
Mechanical Properties of Solids

141014 A rubber cord of density d, Young's modulus $Y$ and length $L$ is suspended vertically. If the cord extends by a length $0.5 \mathrm{~L}$ under its own weight, then $L$ is

1 $\frac{Y}{2 d g}$
2 $\frac{Y}{\mathrm{dg}}$
3 $\frac{2 \mathrm{Y}}{\mathrm{dg}}$
4 $\frac{\mathrm{dg}}{2 \mathrm{Y}}$
5 $\frac{\mathrm{dg}}{\mathrm{Y}}$
Mechanical Properties of Solids

141015 One end of a long metallic wire of length $L$, area of cross-section $A$ and Young's modulus $Y$ is tied to the ceiling. The other end is tied to a massless spring of force constant $k$ and mass $m$ is hung from the free end of the spring. If $m$ is slightly pulled down and released, then its time period of oscillation is

1 $2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$
2 $2 \pi \sqrt{\frac{\mathrm{mYA}}{\mathrm{kL}}}$
3 $2 \pi \sqrt{\frac{\mathrm{m}(\mathrm{kA}+\mathrm{YL})}{\mathrm{kYA}}}$
4 $2 \pi \sqrt{\frac{\mathrm{m}(\mathrm{kL}+\mathrm{YA})}{\mathrm{kYA}}}$
Mechanical Properties of Solids

141017 In a tensile test on a metal bar of diameter $0.015 \mathrm{~m}$ and length $0.2 \mathrm{~m}$, the relation between the load and elongation within the proportional limit is found to be $F=97.2 \times 10^{6}(\Delta L)$, where $F$ is the load (in $N$ ) and $\Delta L$ is the elongation (in $m)$. The Young's modulus of the material in GPa is

1 75.5
2 85.6
3 98.7
4 110
Mechanical Properties of Solids

141012 For a material the ratio of Young's modulus to rigidity modulus is 2.8 . If some force is applied on a wire made of this material. Its crosssectional area decreases by $2 \%$. The percentage change in its length is

1 0.4
2 1.6
3 2.5
4 4
Mechanical Properties of Solids

141014 A rubber cord of density d, Young's modulus $Y$ and length $L$ is suspended vertically. If the cord extends by a length $0.5 \mathrm{~L}$ under its own weight, then $L$ is

1 $\frac{Y}{2 d g}$
2 $\frac{Y}{\mathrm{dg}}$
3 $\frac{2 \mathrm{Y}}{\mathrm{dg}}$
4 $\frac{\mathrm{dg}}{2 \mathrm{Y}}$
5 $\frac{\mathrm{dg}}{\mathrm{Y}}$
Mechanical Properties of Solids

141015 One end of a long metallic wire of length $L$, area of cross-section $A$ and Young's modulus $Y$ is tied to the ceiling. The other end is tied to a massless spring of force constant $k$ and mass $m$ is hung from the free end of the spring. If $m$ is slightly pulled down and released, then its time period of oscillation is

1 $2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$
2 $2 \pi \sqrt{\frac{\mathrm{mYA}}{\mathrm{kL}}}$
3 $2 \pi \sqrt{\frac{\mathrm{m}(\mathrm{kA}+\mathrm{YL})}{\mathrm{kYA}}}$
4 $2 \pi \sqrt{\frac{\mathrm{m}(\mathrm{kL}+\mathrm{YA})}{\mathrm{kYA}}}$
Mechanical Properties of Solids

141017 In a tensile test on a metal bar of diameter $0.015 \mathrm{~m}$ and length $0.2 \mathrm{~m}$, the relation between the load and elongation within the proportional limit is found to be $F=97.2 \times 10^{6}(\Delta L)$, where $F$ is the load (in $N$ ) and $\Delta L$ is the elongation (in $m)$. The Young's modulus of the material in GPa is

1 75.5
2 85.6
3 98.7
4 110
Mechanical Properties of Solids

141012 For a material the ratio of Young's modulus to rigidity modulus is 2.8 . If some force is applied on a wire made of this material. Its crosssectional area decreases by $2 \%$. The percentage change in its length is

1 0.4
2 1.6
3 2.5
4 4
Mechanical Properties of Solids

141014 A rubber cord of density d, Young's modulus $Y$ and length $L$ is suspended vertically. If the cord extends by a length $0.5 \mathrm{~L}$ under its own weight, then $L$ is

1 $\frac{Y}{2 d g}$
2 $\frac{Y}{\mathrm{dg}}$
3 $\frac{2 \mathrm{Y}}{\mathrm{dg}}$
4 $\frac{\mathrm{dg}}{2 \mathrm{Y}}$
5 $\frac{\mathrm{dg}}{\mathrm{Y}}$
Mechanical Properties of Solids

141015 One end of a long metallic wire of length $L$, area of cross-section $A$ and Young's modulus $Y$ is tied to the ceiling. The other end is tied to a massless spring of force constant $k$ and mass $m$ is hung from the free end of the spring. If $m$ is slightly pulled down and released, then its time period of oscillation is

1 $2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$
2 $2 \pi \sqrt{\frac{\mathrm{mYA}}{\mathrm{kL}}}$
3 $2 \pi \sqrt{\frac{\mathrm{m}(\mathrm{kA}+\mathrm{YL})}{\mathrm{kYA}}}$
4 $2 \pi \sqrt{\frac{\mathrm{m}(\mathrm{kL}+\mathrm{YA})}{\mathrm{kYA}}}$
Mechanical Properties of Solids

141017 In a tensile test on a metal bar of diameter $0.015 \mathrm{~m}$ and length $0.2 \mathrm{~m}$, the relation between the load and elongation within the proportional limit is found to be $F=97.2 \times 10^{6}(\Delta L)$, where $F$ is the load (in $N$ ) and $\Delta L$ is the elongation (in $m)$. The Young's modulus of the material in GPa is

1 75.5
2 85.6
3 98.7
4 110