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

140839 One end of a uniform wire of length $L$ and of weight $w$ is attached rigidly to a point in the roof and a weight $w_{1}$ is suspended from its lower end. If $S$ is the area of cross-section of the wire, then the stress in the wire at a height $\frac{3 \mathrm{~L}}{4}$ form its lower end is

1 $\frac{\mathrm{w}_{1}}{\mathrm{~S}}$
2 $\frac{\mathrm{w}_{1}+(\mathrm{w} / 4)}{\mathrm{S}}$
3 $\frac{\mathrm{w}_{1}+(3 \mathrm{w} / 4)}{\mathrm{S}}$
4 $\frac{\mathrm{w}_{1}+\mathrm{w}}{\mathrm{S}}$
Mechanical Properties of Solids

140841 The area of cross section of the rope used to lift a load by a crane is $2.5 \times 10^{-4}$. The maximum lifting capacity of the crane is 10 metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section of the rope should be:
(take $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )

1 $6.25 \times 10^{-4} \mathrm{~m}^{2}$
2 $10 \times 10^{-4} \mathrm{~m}^{2}$
3 $1 \times 10^{-4} \mathrm{~m}^{2}$
4 $1.67 \times 10^{-4} \mathrm{~m}^{2}$
Mechanical Properties of Solids

140842 The force required to stretch a wire of crosssection $1 \mathrm{~cm}^{2}$ to double its length will be:
(Given Yong's modulus of the wire $=$ $\left.2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}\right)$

1 $1 \times 10^{7} \mathrm{~N}$
2 $1.5 \times 10^{7} \mathrm{~N}$
3 $2 \times 10^{7} \mathrm{~N}$
4 $2.5 \times 10^{7} \mathrm{~N}$
Mechanical Properties of Solids

140843 A steel wire of length $3.2 \mathrm{~m}\left(Y_{\mathrm{s}}=2.0 \times 10^{11} \mathrm{Nm}^{-2}\right)$ and a copper wire of length $4.4 \mathrm{~m}\left(Y_{c}=1.1 \times 10^{11}\right.$ $\mathrm{Nm}^{-2}$ ), both of radius $1.4 \mathrm{~mm}$ are connected end to end. When stretched by a load, the net elongation is found to be $1.4 \mathrm{~mm}$. The load applied, in Newton, will be:
(Given $\pi=\frac{22}{7}$ )

1 360
2 180
3 1080
4 154
Mechanical Properties of Solids

140844 A piece of metal having a square cross section of area $400 \mathrm{~mm}^{2}$ is pulled with $40 \mathrm{kN}$ force, producing only elastic deformation. If the Young's modulus of the metal is $40 \times 10^{9} \mathrm{~N} \mathrm{~m}^{-2}$ then the strain is

1 $1 \times 10^{-3}$
2 $1.5 \times 10^{-3}$
3 $2.5 \times 10^{-3}$
4 $4.0 \times 10^{-3}$
Mechanical Properties of Solids

140839 One end of a uniform wire of length $L$ and of weight $w$ is attached rigidly to a point in the roof and a weight $w_{1}$ is suspended from its lower end. If $S$ is the area of cross-section of the wire, then the stress in the wire at a height $\frac{3 \mathrm{~L}}{4}$ form its lower end is

1 $\frac{\mathrm{w}_{1}}{\mathrm{~S}}$
2 $\frac{\mathrm{w}_{1}+(\mathrm{w} / 4)}{\mathrm{S}}$
3 $\frac{\mathrm{w}_{1}+(3 \mathrm{w} / 4)}{\mathrm{S}}$
4 $\frac{\mathrm{w}_{1}+\mathrm{w}}{\mathrm{S}}$
Mechanical Properties of Solids

140841 The area of cross section of the rope used to lift a load by a crane is $2.5 \times 10^{-4}$. The maximum lifting capacity of the crane is 10 metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section of the rope should be:
(take $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )

1 $6.25 \times 10^{-4} \mathrm{~m}^{2}$
2 $10 \times 10^{-4} \mathrm{~m}^{2}$
3 $1 \times 10^{-4} \mathrm{~m}^{2}$
4 $1.67 \times 10^{-4} \mathrm{~m}^{2}$
Mechanical Properties of Solids

140842 The force required to stretch a wire of crosssection $1 \mathrm{~cm}^{2}$ to double its length will be:
(Given Yong's modulus of the wire $=$ $\left.2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}\right)$

1 $1 \times 10^{7} \mathrm{~N}$
2 $1.5 \times 10^{7} \mathrm{~N}$
3 $2 \times 10^{7} \mathrm{~N}$
4 $2.5 \times 10^{7} \mathrm{~N}$
Mechanical Properties of Solids

140843 A steel wire of length $3.2 \mathrm{~m}\left(Y_{\mathrm{s}}=2.0 \times 10^{11} \mathrm{Nm}^{-2}\right)$ and a copper wire of length $4.4 \mathrm{~m}\left(Y_{c}=1.1 \times 10^{11}\right.$ $\mathrm{Nm}^{-2}$ ), both of radius $1.4 \mathrm{~mm}$ are connected end to end. When stretched by a load, the net elongation is found to be $1.4 \mathrm{~mm}$. The load applied, in Newton, will be:
(Given $\pi=\frac{22}{7}$ )

1 360
2 180
3 1080
4 154
Mechanical Properties of Solids

140844 A piece of metal having a square cross section of area $400 \mathrm{~mm}^{2}$ is pulled with $40 \mathrm{kN}$ force, producing only elastic deformation. If the Young's modulus of the metal is $40 \times 10^{9} \mathrm{~N} \mathrm{~m}^{-2}$ then the strain is

1 $1 \times 10^{-3}$
2 $1.5 \times 10^{-3}$
3 $2.5 \times 10^{-3}$
4 $4.0 \times 10^{-3}$
Mechanical Properties of Solids

140839 One end of a uniform wire of length $L$ and of weight $w$ is attached rigidly to a point in the roof and a weight $w_{1}$ is suspended from its lower end. If $S$ is the area of cross-section of the wire, then the stress in the wire at a height $\frac{3 \mathrm{~L}}{4}$ form its lower end is

1 $\frac{\mathrm{w}_{1}}{\mathrm{~S}}$
2 $\frac{\mathrm{w}_{1}+(\mathrm{w} / 4)}{\mathrm{S}}$
3 $\frac{\mathrm{w}_{1}+(3 \mathrm{w} / 4)}{\mathrm{S}}$
4 $\frac{\mathrm{w}_{1}+\mathrm{w}}{\mathrm{S}}$
Mechanical Properties of Solids

140841 The area of cross section of the rope used to lift a load by a crane is $2.5 \times 10^{-4}$. The maximum lifting capacity of the crane is 10 metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section of the rope should be:
(take $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )

1 $6.25 \times 10^{-4} \mathrm{~m}^{2}$
2 $10 \times 10^{-4} \mathrm{~m}^{2}$
3 $1 \times 10^{-4} \mathrm{~m}^{2}$
4 $1.67 \times 10^{-4} \mathrm{~m}^{2}$
Mechanical Properties of Solids

140842 The force required to stretch a wire of crosssection $1 \mathrm{~cm}^{2}$ to double its length will be:
(Given Yong's modulus of the wire $=$ $\left.2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}\right)$

1 $1 \times 10^{7} \mathrm{~N}$
2 $1.5 \times 10^{7} \mathrm{~N}$
3 $2 \times 10^{7} \mathrm{~N}$
4 $2.5 \times 10^{7} \mathrm{~N}$
Mechanical Properties of Solids

140843 A steel wire of length $3.2 \mathrm{~m}\left(Y_{\mathrm{s}}=2.0 \times 10^{11} \mathrm{Nm}^{-2}\right)$ and a copper wire of length $4.4 \mathrm{~m}\left(Y_{c}=1.1 \times 10^{11}\right.$ $\mathrm{Nm}^{-2}$ ), both of radius $1.4 \mathrm{~mm}$ are connected end to end. When stretched by a load, the net elongation is found to be $1.4 \mathrm{~mm}$. The load applied, in Newton, will be:
(Given $\pi=\frac{22}{7}$ )

1 360
2 180
3 1080
4 154
Mechanical Properties of Solids

140844 A piece of metal having a square cross section of area $400 \mathrm{~mm}^{2}$ is pulled with $40 \mathrm{kN}$ force, producing only elastic deformation. If the Young's modulus of the metal is $40 \times 10^{9} \mathrm{~N} \mathrm{~m}^{-2}$ then the strain is

1 $1 \times 10^{-3}$
2 $1.5 \times 10^{-3}$
3 $2.5 \times 10^{-3}$
4 $4.0 \times 10^{-3}$
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Mechanical Properties of Solids

140839 One end of a uniform wire of length $L$ and of weight $w$ is attached rigidly to a point in the roof and a weight $w_{1}$ is suspended from its lower end. If $S$ is the area of cross-section of the wire, then the stress in the wire at a height $\frac{3 \mathrm{~L}}{4}$ form its lower end is

1 $\frac{\mathrm{w}_{1}}{\mathrm{~S}}$
2 $\frac{\mathrm{w}_{1}+(\mathrm{w} / 4)}{\mathrm{S}}$
3 $\frac{\mathrm{w}_{1}+(3 \mathrm{w} / 4)}{\mathrm{S}}$
4 $\frac{\mathrm{w}_{1}+\mathrm{w}}{\mathrm{S}}$
Mechanical Properties of Solids

140841 The area of cross section of the rope used to lift a load by a crane is $2.5 \times 10^{-4}$. The maximum lifting capacity of the crane is 10 metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section of the rope should be:
(take $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )

1 $6.25 \times 10^{-4} \mathrm{~m}^{2}$
2 $10 \times 10^{-4} \mathrm{~m}^{2}$
3 $1 \times 10^{-4} \mathrm{~m}^{2}$
4 $1.67 \times 10^{-4} \mathrm{~m}^{2}$
Mechanical Properties of Solids

140842 The force required to stretch a wire of crosssection $1 \mathrm{~cm}^{2}$ to double its length will be:
(Given Yong's modulus of the wire $=$ $\left.2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}\right)$

1 $1 \times 10^{7} \mathrm{~N}$
2 $1.5 \times 10^{7} \mathrm{~N}$
3 $2 \times 10^{7} \mathrm{~N}$
4 $2.5 \times 10^{7} \mathrm{~N}$
Mechanical Properties of Solids

140843 A steel wire of length $3.2 \mathrm{~m}\left(Y_{\mathrm{s}}=2.0 \times 10^{11} \mathrm{Nm}^{-2}\right)$ and a copper wire of length $4.4 \mathrm{~m}\left(Y_{c}=1.1 \times 10^{11}\right.$ $\mathrm{Nm}^{-2}$ ), both of radius $1.4 \mathrm{~mm}$ are connected end to end. When stretched by a load, the net elongation is found to be $1.4 \mathrm{~mm}$. The load applied, in Newton, will be:
(Given $\pi=\frac{22}{7}$ )

1 360
2 180
3 1080
4 154
Mechanical Properties of Solids

140844 A piece of metal having a square cross section of area $400 \mathrm{~mm}^{2}$ is pulled with $40 \mathrm{kN}$ force, producing only elastic deformation. If the Young's modulus of the metal is $40 \times 10^{9} \mathrm{~N} \mathrm{~m}^{-2}$ then the strain is

1 $1 \times 10^{-3}$
2 $1.5 \times 10^{-3}$
3 $2.5 \times 10^{-3}$
4 $4.0 \times 10^{-3}$
Mechanical Properties of Solids

140839 One end of a uniform wire of length $L$ and of weight $w$ is attached rigidly to a point in the roof and a weight $w_{1}$ is suspended from its lower end. If $S$ is the area of cross-section of the wire, then the stress in the wire at a height $\frac{3 \mathrm{~L}}{4}$ form its lower end is

1 $\frac{\mathrm{w}_{1}}{\mathrm{~S}}$
2 $\frac{\mathrm{w}_{1}+(\mathrm{w} / 4)}{\mathrm{S}}$
3 $\frac{\mathrm{w}_{1}+(3 \mathrm{w} / 4)}{\mathrm{S}}$
4 $\frac{\mathrm{w}_{1}+\mathrm{w}}{\mathrm{S}}$
Mechanical Properties of Solids

140841 The area of cross section of the rope used to lift a load by a crane is $2.5 \times 10^{-4}$. The maximum lifting capacity of the crane is 10 metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section of the rope should be:
(take $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )

1 $6.25 \times 10^{-4} \mathrm{~m}^{2}$
2 $10 \times 10^{-4} \mathrm{~m}^{2}$
3 $1 \times 10^{-4} \mathrm{~m}^{2}$
4 $1.67 \times 10^{-4} \mathrm{~m}^{2}$
Mechanical Properties of Solids

140842 The force required to stretch a wire of crosssection $1 \mathrm{~cm}^{2}$ to double its length will be:
(Given Yong's modulus of the wire $=$ $\left.2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}\right)$

1 $1 \times 10^{7} \mathrm{~N}$
2 $1.5 \times 10^{7} \mathrm{~N}$
3 $2 \times 10^{7} \mathrm{~N}$
4 $2.5 \times 10^{7} \mathrm{~N}$
Mechanical Properties of Solids

140843 A steel wire of length $3.2 \mathrm{~m}\left(Y_{\mathrm{s}}=2.0 \times 10^{11} \mathrm{Nm}^{-2}\right)$ and a copper wire of length $4.4 \mathrm{~m}\left(Y_{c}=1.1 \times 10^{11}\right.$ $\mathrm{Nm}^{-2}$ ), both of radius $1.4 \mathrm{~mm}$ are connected end to end. When stretched by a load, the net elongation is found to be $1.4 \mathrm{~mm}$. The load applied, in Newton, will be:
(Given $\pi=\frac{22}{7}$ )

1 360
2 180
3 1080
4 154
Mechanical Properties of Solids

140844 A piece of metal having a square cross section of area $400 \mathrm{~mm}^{2}$ is pulled with $40 \mathrm{kN}$ force, producing only elastic deformation. If the Young's modulus of the metal is $40 \times 10^{9} \mathrm{~N} \mathrm{~m}^{-2}$ then the strain is

1 $1 \times 10^{-3}$
2 $1.5 \times 10^{-3}$
3 $2.5 \times 10^{-3}$
4 $4.0 \times 10^{-3}$