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

140892 If the work done is stretching a wire by $1 \mathrm{~mm}$ is $2 \mathrm{~J}$, the work necessary for stretching another wire of the same material but double the radius and half the length by $1 \mathbf{~ m m}$ is

1 $4 \mathrm{~J}$
2 $8 \mathrm{~J}$
3 $16 \mathrm{~J}$
4 $\frac{1}{2} \mathrm{~J}$
Mechanical Properties of Solids

140894 The strain stress curves of three wires of different materials are shown in the figure. $P$, $Q$ and $R$ are the elastic limits of the wires. The figure shows that

1 elasticity of wire $P$ is maximum
2 elasticity of wire $\mathrm{Q}$ is maximum
3 tensile strength of $\mathrm{R}$ is maximum
4 None of the above is true
Mechanical Properties of Solids

140896 Two wires of length $l$ and $2 l$, radii $\mathrm{r}$ and $2 \mathrm{r}$ respectively having same Young's modulus are hung with a weight $\mathrm{mg}$. Net elongation is

1 $\frac{3 \mathrm{mg} l}{\pi \mathrm{r}^{2} \mathrm{Y}}$
2 $\frac{2 \mathrm{mg} l}{3 \pi \mathrm{r}^{2} \mathrm{Y}}$
3 $\frac{3 \mathrm{mg} l}{2 \pi \mathrm{r}^{2} \mathrm{Y}}$
4 $\frac{3 \mathrm{mg} l}{4 \pi \mathrm{r}^{2} \mathrm{Y}}$
Mechanical Properties of Solids

140899 What is the maximum possible height of a mountain on the earth if breaking shear stress for a typical rock is $9 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$ and its density is $9 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$. And also shear stress at the base of a mountain is equal to the force per unit area due to its weight? $\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$

1 $5 \mathrm{~km}$
2 $6 \mathrm{~km}$
3 $8 \mathrm{~km}$
4 $10 \mathrm{~km}$
Mechanical Properties of Solids

140900 The diagram below shows the change in the length $X$ of a thin uniform wire caused by the application of stress $F$ at two different temperature $T_{1}$ and $T_{2}$. The variation shown suggests that

1 $\mathrm{T}_{1}>\mathrm{T}_{2}$
2 $\mathrm{T}_{1} \lt \mathrm{T}_{2}$
3 $\mathrm{T}_{2}>\mathrm{T}_{1}$
4 $\mathrm{T}_{1} \geq \mathrm{T}_{2}$
Mechanical Properties of Solids

140892 If the work done is stretching a wire by $1 \mathrm{~mm}$ is $2 \mathrm{~J}$, the work necessary for stretching another wire of the same material but double the radius and half the length by $1 \mathbf{~ m m}$ is

1 $4 \mathrm{~J}$
2 $8 \mathrm{~J}$
3 $16 \mathrm{~J}$
4 $\frac{1}{2} \mathrm{~J}$
Mechanical Properties of Solids

140894 The strain stress curves of three wires of different materials are shown in the figure. $P$, $Q$ and $R$ are the elastic limits of the wires. The figure shows that

1 elasticity of wire $P$ is maximum
2 elasticity of wire $\mathrm{Q}$ is maximum
3 tensile strength of $\mathrm{R}$ is maximum
4 None of the above is true
Mechanical Properties of Solids

140896 Two wires of length $l$ and $2 l$, radii $\mathrm{r}$ and $2 \mathrm{r}$ respectively having same Young's modulus are hung with a weight $\mathrm{mg}$. Net elongation is

1 $\frac{3 \mathrm{mg} l}{\pi \mathrm{r}^{2} \mathrm{Y}}$
2 $\frac{2 \mathrm{mg} l}{3 \pi \mathrm{r}^{2} \mathrm{Y}}$
3 $\frac{3 \mathrm{mg} l}{2 \pi \mathrm{r}^{2} \mathrm{Y}}$
4 $\frac{3 \mathrm{mg} l}{4 \pi \mathrm{r}^{2} \mathrm{Y}}$
Mechanical Properties of Solids

140899 What is the maximum possible height of a mountain on the earth if breaking shear stress for a typical rock is $9 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$ and its density is $9 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$. And also shear stress at the base of a mountain is equal to the force per unit area due to its weight? $\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$

1 $5 \mathrm{~km}$
2 $6 \mathrm{~km}$
3 $8 \mathrm{~km}$
4 $10 \mathrm{~km}$
Mechanical Properties of Solids

140900 The diagram below shows the change in the length $X$ of a thin uniform wire caused by the application of stress $F$ at two different temperature $T_{1}$ and $T_{2}$. The variation shown suggests that

1 $\mathrm{T}_{1}>\mathrm{T}_{2}$
2 $\mathrm{T}_{1} \lt \mathrm{T}_{2}$
3 $\mathrm{T}_{2}>\mathrm{T}_{1}$
4 $\mathrm{T}_{1} \geq \mathrm{T}_{2}$
Mechanical Properties of Solids

140892 If the work done is stretching a wire by $1 \mathrm{~mm}$ is $2 \mathrm{~J}$, the work necessary for stretching another wire of the same material but double the radius and half the length by $1 \mathbf{~ m m}$ is

1 $4 \mathrm{~J}$
2 $8 \mathrm{~J}$
3 $16 \mathrm{~J}$
4 $\frac{1}{2} \mathrm{~J}$
Mechanical Properties of Solids

140894 The strain stress curves of three wires of different materials are shown in the figure. $P$, $Q$ and $R$ are the elastic limits of the wires. The figure shows that

1 elasticity of wire $P$ is maximum
2 elasticity of wire $\mathrm{Q}$ is maximum
3 tensile strength of $\mathrm{R}$ is maximum
4 None of the above is true
Mechanical Properties of Solids

140896 Two wires of length $l$ and $2 l$, radii $\mathrm{r}$ and $2 \mathrm{r}$ respectively having same Young's modulus are hung with a weight $\mathrm{mg}$. Net elongation is

1 $\frac{3 \mathrm{mg} l}{\pi \mathrm{r}^{2} \mathrm{Y}}$
2 $\frac{2 \mathrm{mg} l}{3 \pi \mathrm{r}^{2} \mathrm{Y}}$
3 $\frac{3 \mathrm{mg} l}{2 \pi \mathrm{r}^{2} \mathrm{Y}}$
4 $\frac{3 \mathrm{mg} l}{4 \pi \mathrm{r}^{2} \mathrm{Y}}$
Mechanical Properties of Solids

140899 What is the maximum possible height of a mountain on the earth if breaking shear stress for a typical rock is $9 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$ and its density is $9 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$. And also shear stress at the base of a mountain is equal to the force per unit area due to its weight? $\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$

1 $5 \mathrm{~km}$
2 $6 \mathrm{~km}$
3 $8 \mathrm{~km}$
4 $10 \mathrm{~km}$
Mechanical Properties of Solids

140900 The diagram below shows the change in the length $X$ of a thin uniform wire caused by the application of stress $F$ at two different temperature $T_{1}$ and $T_{2}$. The variation shown suggests that

1 $\mathrm{T}_{1}>\mathrm{T}_{2}$
2 $\mathrm{T}_{1} \lt \mathrm{T}_{2}$
3 $\mathrm{T}_{2}>\mathrm{T}_{1}$
4 $\mathrm{T}_{1} \geq \mathrm{T}_{2}$
Mechanical Properties of Solids

140892 If the work done is stretching a wire by $1 \mathrm{~mm}$ is $2 \mathrm{~J}$, the work necessary for stretching another wire of the same material but double the radius and half the length by $1 \mathbf{~ m m}$ is

1 $4 \mathrm{~J}$
2 $8 \mathrm{~J}$
3 $16 \mathrm{~J}$
4 $\frac{1}{2} \mathrm{~J}$
Mechanical Properties of Solids

140894 The strain stress curves of three wires of different materials are shown in the figure. $P$, $Q$ and $R$ are the elastic limits of the wires. The figure shows that

1 elasticity of wire $P$ is maximum
2 elasticity of wire $\mathrm{Q}$ is maximum
3 tensile strength of $\mathrm{R}$ is maximum
4 None of the above is true
Mechanical Properties of Solids

140896 Two wires of length $l$ and $2 l$, radii $\mathrm{r}$ and $2 \mathrm{r}$ respectively having same Young's modulus are hung with a weight $\mathrm{mg}$. Net elongation is

1 $\frac{3 \mathrm{mg} l}{\pi \mathrm{r}^{2} \mathrm{Y}}$
2 $\frac{2 \mathrm{mg} l}{3 \pi \mathrm{r}^{2} \mathrm{Y}}$
3 $\frac{3 \mathrm{mg} l}{2 \pi \mathrm{r}^{2} \mathrm{Y}}$
4 $\frac{3 \mathrm{mg} l}{4 \pi \mathrm{r}^{2} \mathrm{Y}}$
Mechanical Properties of Solids

140899 What is the maximum possible height of a mountain on the earth if breaking shear stress for a typical rock is $9 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$ and its density is $9 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$. And also shear stress at the base of a mountain is equal to the force per unit area due to its weight? $\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$

1 $5 \mathrm{~km}$
2 $6 \mathrm{~km}$
3 $8 \mathrm{~km}$
4 $10 \mathrm{~km}$
Mechanical Properties of Solids

140900 The diagram below shows the change in the length $X$ of a thin uniform wire caused by the application of stress $F$ at two different temperature $T_{1}$ and $T_{2}$. The variation shown suggests that

1 $\mathrm{T}_{1}>\mathrm{T}_{2}$
2 $\mathrm{T}_{1} \lt \mathrm{T}_{2}$
3 $\mathrm{T}_{2}>\mathrm{T}_{1}$
4 $\mathrm{T}_{1} \geq \mathrm{T}_{2}$
Mechanical Properties of Solids

140892 If the work done is stretching a wire by $1 \mathrm{~mm}$ is $2 \mathrm{~J}$, the work necessary for stretching another wire of the same material but double the radius and half the length by $1 \mathbf{~ m m}$ is

1 $4 \mathrm{~J}$
2 $8 \mathrm{~J}$
3 $16 \mathrm{~J}$
4 $\frac{1}{2} \mathrm{~J}$
Mechanical Properties of Solids

140894 The strain stress curves of three wires of different materials are shown in the figure. $P$, $Q$ and $R$ are the elastic limits of the wires. The figure shows that

1 elasticity of wire $P$ is maximum
2 elasticity of wire $\mathrm{Q}$ is maximum
3 tensile strength of $\mathrm{R}$ is maximum
4 None of the above is true
Mechanical Properties of Solids

140896 Two wires of length $l$ and $2 l$, radii $\mathrm{r}$ and $2 \mathrm{r}$ respectively having same Young's modulus are hung with a weight $\mathrm{mg}$. Net elongation is

1 $\frac{3 \mathrm{mg} l}{\pi \mathrm{r}^{2} \mathrm{Y}}$
2 $\frac{2 \mathrm{mg} l}{3 \pi \mathrm{r}^{2} \mathrm{Y}}$
3 $\frac{3 \mathrm{mg} l}{2 \pi \mathrm{r}^{2} \mathrm{Y}}$
4 $\frac{3 \mathrm{mg} l}{4 \pi \mathrm{r}^{2} \mathrm{Y}}$
Mechanical Properties of Solids

140899 What is the maximum possible height of a mountain on the earth if breaking shear stress for a typical rock is $9 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$ and its density is $9 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$. And also shear stress at the base of a mountain is equal to the force per unit area due to its weight? $\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$

1 $5 \mathrm{~km}$
2 $6 \mathrm{~km}$
3 $8 \mathrm{~km}$
4 $10 \mathrm{~km}$
Mechanical Properties of Solids

140900 The diagram below shows the change in the length $X$ of a thin uniform wire caused by the application of stress $F$ at two different temperature $T_{1}$ and $T_{2}$. The variation shown suggests that

1 $\mathrm{T}_{1}>\mathrm{T}_{2}$
2 $\mathrm{T}_{1} \lt \mathrm{T}_{2}$
3 $\mathrm{T}_{2}>\mathrm{T}_{1}$
4 $\mathrm{T}_{1} \geq \mathrm{T}_{2}$