# 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 |
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The bulk modulus of water is . The increase in pressure required to decrease the volume of water sample by 0.1% is:-

1. $$4\times 10^{6}N/m^{2}$$

2. $$2\times 10^{6}N/m^{2}$$

3. $$2\times 10^{8}N/m^{2}$$

4. $$8\times 10^{6}N/m^{2}$$

Subtopic:  Shear and bulk modulus |
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To break a wire, a force of is required. If the density of the material is , 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 |
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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 0N 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 |
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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 $∆\mathrm{l}$ 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 |
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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 'Δl'. Which of the following graph is a straight line?

1.

2.

3.

4.

Subtopic:  Young's modulus |
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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:
()

1.

2.

3.

4.  3.9

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 |
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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 |
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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 |
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