00. Elasticity, Stress, Strain and Hooke's law
Mechanical Properties of Solids

140875 Two equal and opposite force each $F$ act on a rod of uniform cross-sectional area $A$ as shown in the figure. Shearing stress on the section $A B$ will be

1 $\frac{\mathrm{F} \sin \theta \cos \theta}{\mathrm{A}}$
2 $\frac{\mathrm{F} \sin \theta}{\mathrm{A}}$
3 $\frac{F \cos \theta}{\mathrm{A}}$
4 $\frac{F \sin ^{2} \theta}{\mathrm{A}}$
Mechanical Properties of Solids

140876 A rubber (eraser) $3 \mathrm{~cm} \times 1 \mathrm{~cm} \times 8 \mathrm{~cm}$ is clamped at one end with $8 \mathrm{~cm}$ edge vertical. A horizontal force of $2.4 \mathrm{~N}$ is applied at the free end (the top face). If the shear modulus of the rubber is $1.6 \times 10^{5} \mathrm{Nm}^{-2}$ then the horizontal displacement of the top face will be

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

140877 Young's modulus experiment is performed on a steel wire of $1 \mathrm{~m}$ length and $8 \mathrm{~mm}$ diameter. The mass required to be added in the experiment to produce $5 \mathrm{~mm}$ elongation of the wire of $\left(Y_{\text {steel }}=2 \times 10^{9} \mathrm{Nm}^{-2}, g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$

1 $25 \mathrm{~kg}$
2 $50 \mathrm{~kg}$
3 $250 \mathrm{~kg}$
4 $500 \mathrm{~kg}$
TS-
Mechanical Properties of Solids

140879 Assertion: The stress-strain graphs are shown in the figure for two materials A and B are shown in figure. Young's modulus of A is greater than that of B.

Reason: The Young's modules for small strain is, $\mathrm{Y}=\frac{\text { stress }}{\text { strain }}=$ slope of linear portion, of graph; and slope of A is less than slope that of B.

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.
Mechanical Properties of Solids

140880 The length of elastic string, obeying Hooke's law is $\ell_{1}$ meters when the tension $4 \mathrm{~N}$ and $l_{2}$ meters when the tension is $5 \mathrm{~N}$. The length in meters when the tension is $9 \mathrm{~N}$ is-

1 $5 \ell_{1}-4 \ell_{2}$
2 $5 \ell_{2}-4 \ell_{1}$
3 $9 \ell_{1}-8 \ell_{2}$
4 $9 \ell_{2}-8 \ell_{1}$
Mechanical Properties of Solids

140875 Two equal and opposite force each $F$ act on a rod of uniform cross-sectional area $A$ as shown in the figure. Shearing stress on the section $A B$ will be

1 $\frac{\mathrm{F} \sin \theta \cos \theta}{\mathrm{A}}$
2 $\frac{\mathrm{F} \sin \theta}{\mathrm{A}}$
3 $\frac{F \cos \theta}{\mathrm{A}}$
4 $\frac{F \sin ^{2} \theta}{\mathrm{A}}$
Mechanical Properties of Solids

140876 A rubber (eraser) $3 \mathrm{~cm} \times 1 \mathrm{~cm} \times 8 \mathrm{~cm}$ is clamped at one end with $8 \mathrm{~cm}$ edge vertical. A horizontal force of $2.4 \mathrm{~N}$ is applied at the free end (the top face). If the shear modulus of the rubber is $1.6 \times 10^{5} \mathrm{Nm}^{-2}$ then the horizontal displacement of the top face will be

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

140877 Young's modulus experiment is performed on a steel wire of $1 \mathrm{~m}$ length and $8 \mathrm{~mm}$ diameter. The mass required to be added in the experiment to produce $5 \mathrm{~mm}$ elongation of the wire of $\left(Y_{\text {steel }}=2 \times 10^{9} \mathrm{Nm}^{-2}, g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$

1 $25 \mathrm{~kg}$
2 $50 \mathrm{~kg}$
3 $250 \mathrm{~kg}$
4 $500 \mathrm{~kg}$
TS-
Mechanical Properties of Solids

140879 Assertion: The stress-strain graphs are shown in the figure for two materials A and B are shown in figure. Young's modulus of A is greater than that of B.

Reason: The Young's modules for small strain is, $\mathrm{Y}=\frac{\text { stress }}{\text { strain }}=$ slope of linear portion, of graph; and slope of A is less than slope that of B.

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.
Mechanical Properties of Solids

140880 The length of elastic string, obeying Hooke's law is $\ell_{1}$ meters when the tension $4 \mathrm{~N}$ and $l_{2}$ meters when the tension is $5 \mathrm{~N}$. The length in meters when the tension is $9 \mathrm{~N}$ is-

1 $5 \ell_{1}-4 \ell_{2}$
2 $5 \ell_{2}-4 \ell_{1}$
3 $9 \ell_{1}-8 \ell_{2}$
4 $9 \ell_{2}-8 \ell_{1}$
Mechanical Properties of Solids

140875 Two equal and opposite force each $F$ act on a rod of uniform cross-sectional area $A$ as shown in the figure. Shearing stress on the section $A B$ will be

1 $\frac{\mathrm{F} \sin \theta \cos \theta}{\mathrm{A}}$
2 $\frac{\mathrm{F} \sin \theta}{\mathrm{A}}$
3 $\frac{F \cos \theta}{\mathrm{A}}$
4 $\frac{F \sin ^{2} \theta}{\mathrm{A}}$
Mechanical Properties of Solids

140876 A rubber (eraser) $3 \mathrm{~cm} \times 1 \mathrm{~cm} \times 8 \mathrm{~cm}$ is clamped at one end with $8 \mathrm{~cm}$ edge vertical. A horizontal force of $2.4 \mathrm{~N}$ is applied at the free end (the top face). If the shear modulus of the rubber is $1.6 \times 10^{5} \mathrm{Nm}^{-2}$ then the horizontal displacement of the top face will be

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

140877 Young's modulus experiment is performed on a steel wire of $1 \mathrm{~m}$ length and $8 \mathrm{~mm}$ diameter. The mass required to be added in the experiment to produce $5 \mathrm{~mm}$ elongation of the wire of $\left(Y_{\text {steel }}=2 \times 10^{9} \mathrm{Nm}^{-2}, g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$

1 $25 \mathrm{~kg}$
2 $50 \mathrm{~kg}$
3 $250 \mathrm{~kg}$
4 $500 \mathrm{~kg}$
TS-
Mechanical Properties of Solids

140879 Assertion: The stress-strain graphs are shown in the figure for two materials A and B are shown in figure. Young's modulus of A is greater than that of B.

Reason: The Young's modules for small strain is, $\mathrm{Y}=\frac{\text { stress }}{\text { strain }}=$ slope of linear portion, of graph; and slope of A is less than slope that of B.

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.
Mechanical Properties of Solids

140880 The length of elastic string, obeying Hooke's law is $\ell_{1}$ meters when the tension $4 \mathrm{~N}$ and $l_{2}$ meters when the tension is $5 \mathrm{~N}$. The length in meters when the tension is $9 \mathrm{~N}$ is-

1 $5 \ell_{1}-4 \ell_{2}$
2 $5 \ell_{2}-4 \ell_{1}$
3 $9 \ell_{1}-8 \ell_{2}$
4 $9 \ell_{2}-8 \ell_{1}$
Mechanical Properties of Solids

140875 Two equal and opposite force each $F$ act on a rod of uniform cross-sectional area $A$ as shown in the figure. Shearing stress on the section $A B$ will be

1 $\frac{\mathrm{F} \sin \theta \cos \theta}{\mathrm{A}}$
2 $\frac{\mathrm{F} \sin \theta}{\mathrm{A}}$
3 $\frac{F \cos \theta}{\mathrm{A}}$
4 $\frac{F \sin ^{2} \theta}{\mathrm{A}}$
Mechanical Properties of Solids

140876 A rubber (eraser) $3 \mathrm{~cm} \times 1 \mathrm{~cm} \times 8 \mathrm{~cm}$ is clamped at one end with $8 \mathrm{~cm}$ edge vertical. A horizontal force of $2.4 \mathrm{~N}$ is applied at the free end (the top face). If the shear modulus of the rubber is $1.6 \times 10^{5} \mathrm{Nm}^{-2}$ then the horizontal displacement of the top face will be

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

140877 Young's modulus experiment is performed on a steel wire of $1 \mathrm{~m}$ length and $8 \mathrm{~mm}$ diameter. The mass required to be added in the experiment to produce $5 \mathrm{~mm}$ elongation of the wire of $\left(Y_{\text {steel }}=2 \times 10^{9} \mathrm{Nm}^{-2}, g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$

1 $25 \mathrm{~kg}$
2 $50 \mathrm{~kg}$
3 $250 \mathrm{~kg}$
4 $500 \mathrm{~kg}$
TS-
Mechanical Properties of Solids

140879 Assertion: The stress-strain graphs are shown in the figure for two materials A and B are shown in figure. Young's modulus of A is greater than that of B.

Reason: The Young's modules for small strain is, $\mathrm{Y}=\frac{\text { stress }}{\text { strain }}=$ slope of linear portion, of graph; and slope of A is less than slope that of B.

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.
Mechanical Properties of Solids

140880 The length of elastic string, obeying Hooke's law is $\ell_{1}$ meters when the tension $4 \mathrm{~N}$ and $l_{2}$ meters when the tension is $5 \mathrm{~N}$. The length in meters when the tension is $9 \mathrm{~N}$ is-

1 $5 \ell_{1}-4 \ell_{2}$
2 $5 \ell_{2}-4 \ell_{1}$
3 $9 \ell_{1}-8 \ell_{2}$
4 $9 \ell_{2}-8 \ell_{1}$
Mechanical Properties of Solids

140875 Two equal and opposite force each $F$ act on a rod of uniform cross-sectional area $A$ as shown in the figure. Shearing stress on the section $A B$ will be

1 $\frac{\mathrm{F} \sin \theta \cos \theta}{\mathrm{A}}$
2 $\frac{\mathrm{F} \sin \theta}{\mathrm{A}}$
3 $\frac{F \cos \theta}{\mathrm{A}}$
4 $\frac{F \sin ^{2} \theta}{\mathrm{A}}$
Mechanical Properties of Solids

140876 A rubber (eraser) $3 \mathrm{~cm} \times 1 \mathrm{~cm} \times 8 \mathrm{~cm}$ is clamped at one end with $8 \mathrm{~cm}$ edge vertical. A horizontal force of $2.4 \mathrm{~N}$ is applied at the free end (the top face). If the shear modulus of the rubber is $1.6 \times 10^{5} \mathrm{Nm}^{-2}$ then the horizontal displacement of the top face will be

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

140877 Young's modulus experiment is performed on a steel wire of $1 \mathrm{~m}$ length and $8 \mathrm{~mm}$ diameter. The mass required to be added in the experiment to produce $5 \mathrm{~mm}$ elongation of the wire of $\left(Y_{\text {steel }}=2 \times 10^{9} \mathrm{Nm}^{-2}, g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$

1 $25 \mathrm{~kg}$
2 $50 \mathrm{~kg}$
3 $250 \mathrm{~kg}$
4 $500 \mathrm{~kg}$
TS-
Mechanical Properties of Solids

140879 Assertion: The stress-strain graphs are shown in the figure for two materials A and B are shown in figure. Young's modulus of A is greater than that of B.

Reason: The Young's modules for small strain is, $\mathrm{Y}=\frac{\text { stress }}{\text { strain }}=$ slope of linear portion, of graph; and slope of A is less than slope that of B.

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.
Mechanical Properties of Solids

140880 The length of elastic string, obeying Hooke's law is $\ell_{1}$ meters when the tension $4 \mathrm{~N}$ and $l_{2}$ meters when the tension is $5 \mathrm{~N}$. The length in meters when the tension is $9 \mathrm{~N}$ is-

1 $5 \ell_{1}-4 \ell_{2}$
2 $5 \ell_{2}-4 \ell_{1}$
3 $9 \ell_{1}-8 \ell_{2}$
4 $9 \ell_{2}-8 \ell_{1}$