141019
An iron rod of length $2 \mathrm{~m}$ and cross-sectional area of $50 \mathrm{~mm}^{2}$ stretched by $0.5 \mathrm{~mm}$, when a mass of $250 \mathrm{~kg}$ is hung from its lower end. Young's modulus of iron rod is:
B Given, Velocity of ball $=(4 \hat{i}+4 \hat{j}) \mathrm{m} / \mathrm{s}$ Coefficient of restitution $(\mathrm{e})=\frac{1}{2}$ We know that, $\mathrm{e}=\frac{\mathrm{v}_{\text {separation }}}{\mathrm{v}_{\text {approach }}}$ $\frac{1}{2}=\frac{\mathrm{v}_{\mathrm{y}}-0}{4-0} \quad[\mathrm{u}=4]$ $\mathrm{v}_{\mathrm{y}}=2$ and $\mathrm{v}_{\mathrm{x}}$ will remain same, Hence, $\overrightarrow{\mathrm{v}}_{\text {final }}=4 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}$
UPSEE - 2017]
Mechanical Properties of Solids
141021
Take, bulk modulus of water $B=2100 \mathrm{MPa}$. What increase in pressure is required to decrease the volume of 200 liters of water by 0.004 percent?
141018
Assertion: Solids are least compressible and gases are most compressible. Reason: solids have definite shape and volume but gases do not have either definite shape or definite volume.
1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Explanation:
B The incompressibility of solids is primarily due to the tight coupling between the neighbouring atoms. Molecules in gases are very poorly coupled to their neighbours.
AIIMS-2017
Mechanical Properties of Solids
141023
The bulk modulus of a liquid of density 8000 $\mathrm{kgm}^{-3}$ is $2 \times 10^{9} \mathrm{Nm}^{-2}$. The speed of sound in that liquid is (in $\mathrm{ms}^{-1}$ )
1 200
2 250
3 100
4 350
5 500
Explanation:
E Given, Density $(\rho)=8000 \mathrm{~kg} / \mathrm{m}^{3}$ and Bulk modulus $(B)=2 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$ We know, $\mathrm{v}=\sqrt{\frac{\mathrm{B}}{\rho}}$ $\mathrm{v}=\sqrt{\frac{2 \times 10^{9}}{8000}}$ $\mathrm{v}=\frac{1000}{2}$ $\mathrm{v}=500 \mathrm{~m} / \mathrm{sec}$
141019
An iron rod of length $2 \mathrm{~m}$ and cross-sectional area of $50 \mathrm{~mm}^{2}$ stretched by $0.5 \mathrm{~mm}$, when a mass of $250 \mathrm{~kg}$ is hung from its lower end. Young's modulus of iron rod is:
B Given, Velocity of ball $=(4 \hat{i}+4 \hat{j}) \mathrm{m} / \mathrm{s}$ Coefficient of restitution $(\mathrm{e})=\frac{1}{2}$ We know that, $\mathrm{e}=\frac{\mathrm{v}_{\text {separation }}}{\mathrm{v}_{\text {approach }}}$ $\frac{1}{2}=\frac{\mathrm{v}_{\mathrm{y}}-0}{4-0} \quad[\mathrm{u}=4]$ $\mathrm{v}_{\mathrm{y}}=2$ and $\mathrm{v}_{\mathrm{x}}$ will remain same, Hence, $\overrightarrow{\mathrm{v}}_{\text {final }}=4 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}$
UPSEE - 2017]
Mechanical Properties of Solids
141021
Take, bulk modulus of water $B=2100 \mathrm{MPa}$. What increase in pressure is required to decrease the volume of 200 liters of water by 0.004 percent?
141018
Assertion: Solids are least compressible and gases are most compressible. Reason: solids have definite shape and volume but gases do not have either definite shape or definite volume.
1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Explanation:
B The incompressibility of solids is primarily due to the tight coupling between the neighbouring atoms. Molecules in gases are very poorly coupled to their neighbours.
AIIMS-2017
Mechanical Properties of Solids
141023
The bulk modulus of a liquid of density 8000 $\mathrm{kgm}^{-3}$ is $2 \times 10^{9} \mathrm{Nm}^{-2}$. The speed of sound in that liquid is (in $\mathrm{ms}^{-1}$ )
1 200
2 250
3 100
4 350
5 500
Explanation:
E Given, Density $(\rho)=8000 \mathrm{~kg} / \mathrm{m}^{3}$ and Bulk modulus $(B)=2 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$ We know, $\mathrm{v}=\sqrt{\frac{\mathrm{B}}{\rho}}$ $\mathrm{v}=\sqrt{\frac{2 \times 10^{9}}{8000}}$ $\mathrm{v}=\frac{1000}{2}$ $\mathrm{v}=500 \mathrm{~m} / \mathrm{sec}$
141019
An iron rod of length $2 \mathrm{~m}$ and cross-sectional area of $50 \mathrm{~mm}^{2}$ stretched by $0.5 \mathrm{~mm}$, when a mass of $250 \mathrm{~kg}$ is hung from its lower end. Young's modulus of iron rod is:
B Given, Velocity of ball $=(4 \hat{i}+4 \hat{j}) \mathrm{m} / \mathrm{s}$ Coefficient of restitution $(\mathrm{e})=\frac{1}{2}$ We know that, $\mathrm{e}=\frac{\mathrm{v}_{\text {separation }}}{\mathrm{v}_{\text {approach }}}$ $\frac{1}{2}=\frac{\mathrm{v}_{\mathrm{y}}-0}{4-0} \quad[\mathrm{u}=4]$ $\mathrm{v}_{\mathrm{y}}=2$ and $\mathrm{v}_{\mathrm{x}}$ will remain same, Hence, $\overrightarrow{\mathrm{v}}_{\text {final }}=4 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}$
UPSEE - 2017]
Mechanical Properties of Solids
141021
Take, bulk modulus of water $B=2100 \mathrm{MPa}$. What increase in pressure is required to decrease the volume of 200 liters of water by 0.004 percent?
141018
Assertion: Solids are least compressible and gases are most compressible. Reason: solids have definite shape and volume but gases do not have either definite shape or definite volume.
1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Explanation:
B The incompressibility of solids is primarily due to the tight coupling between the neighbouring atoms. Molecules in gases are very poorly coupled to their neighbours.
AIIMS-2017
Mechanical Properties of Solids
141023
The bulk modulus of a liquid of density 8000 $\mathrm{kgm}^{-3}$ is $2 \times 10^{9} \mathrm{Nm}^{-2}$. The speed of sound in that liquid is (in $\mathrm{ms}^{-1}$ )
1 200
2 250
3 100
4 350
5 500
Explanation:
E Given, Density $(\rho)=8000 \mathrm{~kg} / \mathrm{m}^{3}$ and Bulk modulus $(B)=2 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$ We know, $\mathrm{v}=\sqrt{\frac{\mathrm{B}}{\rho}}$ $\mathrm{v}=\sqrt{\frac{2 \times 10^{9}}{8000}}$ $\mathrm{v}=\frac{1000}{2}$ $\mathrm{v}=500 \mathrm{~m} / \mathrm{sec}$
141019
An iron rod of length $2 \mathrm{~m}$ and cross-sectional area of $50 \mathrm{~mm}^{2}$ stretched by $0.5 \mathrm{~mm}$, when a mass of $250 \mathrm{~kg}$ is hung from its lower end. Young's modulus of iron rod is:
B Given, Velocity of ball $=(4 \hat{i}+4 \hat{j}) \mathrm{m} / \mathrm{s}$ Coefficient of restitution $(\mathrm{e})=\frac{1}{2}$ We know that, $\mathrm{e}=\frac{\mathrm{v}_{\text {separation }}}{\mathrm{v}_{\text {approach }}}$ $\frac{1}{2}=\frac{\mathrm{v}_{\mathrm{y}}-0}{4-0} \quad[\mathrm{u}=4]$ $\mathrm{v}_{\mathrm{y}}=2$ and $\mathrm{v}_{\mathrm{x}}$ will remain same, Hence, $\overrightarrow{\mathrm{v}}_{\text {final }}=4 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}$
UPSEE - 2017]
Mechanical Properties of Solids
141021
Take, bulk modulus of water $B=2100 \mathrm{MPa}$. What increase in pressure is required to decrease the volume of 200 liters of water by 0.004 percent?
141018
Assertion: Solids are least compressible and gases are most compressible. Reason: solids have definite shape and volume but gases do not have either definite shape or definite volume.
1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Explanation:
B The incompressibility of solids is primarily due to the tight coupling between the neighbouring atoms. Molecules in gases are very poorly coupled to their neighbours.
AIIMS-2017
Mechanical Properties of Solids
141023
The bulk modulus of a liquid of density 8000 $\mathrm{kgm}^{-3}$ is $2 \times 10^{9} \mathrm{Nm}^{-2}$. The speed of sound in that liquid is (in $\mathrm{ms}^{-1}$ )
1 200
2 250
3 100
4 350
5 500
Explanation:
E Given, Density $(\rho)=8000 \mathrm{~kg} / \mathrm{m}^{3}$ and Bulk modulus $(B)=2 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$ We know, $\mathrm{v}=\sqrt{\frac{\mathrm{B}}{\rho}}$ $\mathrm{v}=\sqrt{\frac{2 \times 10^{9}}{8000}}$ $\mathrm{v}=\frac{1000}{2}$ $\mathrm{v}=500 \mathrm{~m} / \mathrm{sec}$
