# 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 W1 is suspended from its lower end. If A is the area of cross-section of the wire , the stress in the wire at a height 3L/4 from its lower end is: 1.  $\frac{\mathrm{W}+{\mathrm{W}}_{1}}{\mathrm{A}}$ 2.  $\frac{4\mathrm{W}+{\mathrm{W}}_{1}}{3\mathrm{A}}$ 3.  $\frac{3\mathrm{W}+{\mathrm{W}}_{1}}{4\mathrm{A}}$ 4.  $\frac{\frac{3}{4}\mathrm{W}+{\mathrm{W}}_{1}}{\mathrm{A}}$

Subtopic:  Stress - Strain |
70%
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The bulk modulus of water is $2×{10}^{9}$ $\mathrm{N}/{\mathrm{m}}^{2}$. The increase in pressure required to decrease the volume of water sample by $$0.1$$% is:
1. $$4 \times 10^6 \mathrm{~N} / \mathrm{m}^2$$
2. $$2 \times 10^{\mathrm{6}}~ \mathrm{N} / \mathrm{m}^2$$
3. $$2 \times 10^{\mathrm{8}}~ \mathrm{N} / \mathrm{m}^2$$
4. $$8 \times 10^{\mathrm{6}}~ \mathrm{N} / \mathrm{m}^2$$

Subtopic:  Shear and bulk modulus |
84%
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To break a wire, a force of ${10}^{6}$ $N/{m}^{2}$ is required. If the density of the material is $3×{10}^{3}$ $kg/{m}^{3}$, then the length of the wire which will break by its own weight will be:

1. 34 m

2. 30 m

3. 300 m

4. 3 m

Subtopic:  Stress - Strain |
61%
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The length of elastic string, obeying Hooke's law is ${l}_{1}$ metres when the tension is 4N, and ${l}_{2}$ metres when the tension is 5N. The length in metres when the tension is 0 N will be:

1. $5{l}_{1}-4{l}_{2}$

2. $5{l}_{2}-4{l}_{1}$

3. $9{l}_{1}-8{l}_{2}$

4. $9{l}_{2}-8{l}_{1}$

Subtopic:  Hooke's Law |
63%
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Two wires are made of the same material and have the same volume. The first wire has a cross-sectional area $$A$$ and the second wire has a cross-sectional area $$3A$$. If the length of the first wire is increased by $$\Delta l$$ on applying a force $$F$$, how much force is needed to stretch the second wire by the same amount?

 1 $$9F$$ 2 $$6F$$ 3 $$4F$$ 4 $$F$$
Subtopic:  Young's modulus |
76%
From NCERT
NEET - 2018
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Copper of fixed volume $$V$$ is drawn into a wire of length $$l.$$ When this wire is subjected to a constant force $$F,$$ the extension produced in the wire is $$\Delta l.$$ Which of the following graphs is a straight line?
1. $$\Delta l ~\text{vs}~\frac{1}{l}$$
2. $$\Delta l ~\text{vs}~l^2$$
3. $$\Delta l ~\text{vs}~\frac{1}{l^2}$$
4. $$\Delta l ~\text{vs}~l$$

Subtopic:  Young's modulus |
70%
From NCERT
AIPMT - 2014
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Overall changes in volume and radius of a uniform cylindrical steel wire are 0.2% and 0.002% respectively when subjected to some suitable force. Longitudinal tensile stress acting on the wire is: ($\mathrm{Y}=2.0×{10}^{11}$ ${\mathrm{Nm}}^{-2}$)

1.  $3.2×{10}^{11}$ ${\mathrm{Nm}}^{-2}$

2.  $3.2×{10}^{7}$ ${\mathrm{Nm}}^{-2}$

3.  $3.6×{10}^{9}$ ${\mathrm{Nm}}^{-2}$

4.  3.9$×{10}^{8}$ ${\mathrm{Nm}}^{-2}$

Subtopic:  Young's modulus |
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A 1000 kg lift is tied with metallic wires of maximum safe stress of 1.4 $×$ 108 N m-2. If the maximum acceleration of the lift is 1.2 m s-2, then the minimum diameter of the wire is:
1. 1 m

2. 0.1 m

3. 0.01 m

4. 0.001 m

Subtopic:  Stress - Strain |
55%
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A wire can sustain a weight of 10 kg before breaking. If the wire is cut into two equal parts, then each part can sustain a weight of:

 1 2.5 kg 2 5 kg 3 10 kg 4 15 kg
Subtopic:  Stress - Strain |
72%
From NCERT
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A uniform cylinder rod of length L, cross-sectional area A and Young's modulus Y is acted upon by the forces, as shown in the figure. The elongation of the rod is:

1. $\frac{3FL}{5AY}$

2. $\frac{2FL}{5AY}$

3. $\frac{2FL}{8AY}$

4. $\frac{8FL}{3AY}$

Subtopic:  Young's modulus |
57%
From NCERT
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