# 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 $$A$$ is the area of cross-section of the wire, the stress in the wire at a height $$\frac{3L}{4}$$ from its lower end is: 1. $$\frac{W+W_1}{A}$$ 2. $$\frac{4W+W_1}{3A}$$ 3. $$\frac{3W+W_1}{4A}$$ 4. $$\frac{\frac{3}{4}W+W_1}{A}$$

Subtopic:  Stress - Strain |
71%
From NCERT
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The bulk modulus of water is $$2\times 10^{9}~\text{N/m}^2$$${}^{}$. The increase in pressure required to decrease the volume of water sample by $$0.1\%$$ is:
1. $$4 \times 10^{6}~\text{N/m}^2$$
2. $$2 \times 10^{6}~\text{N/m}^2$$
3. $$2 \times 10^{8}~\text{N/m}^2$$
4. $$8 \times 10^{6}~\text{N/m}^2$$

Subtopic:  Shear and bulk modulus |
84%
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To break a wire, a force of $$10^6~\text{N/m}^{2}$$ is required. If the density of the material is $$3\times 10^{3}~\text{kg/m}^3,$$ 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 $$4~\text{N}$$, and $$l_2$$ metres when the tension is $$5~\text{N}$$. The length in metres when the tension is $$0~\text{N}$$ will be:
1. $$5l_1-4l_2$$
2. $$5l_2-4l_1$$
3. $$9l_1-8l_2$$
4. $$9l_2-8l_1$$

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: $$\left(2.0\times 10^{11}~\text{Nm}^{-2}\right)$$
1. $$3.2\times 10^{11}~\text{Nm}^{-2}$$
2. $$3.2\times 10^{7}~\text{Nm}^{-2}$$
3. $$3.6\times 10^{9}~\text{Nm}^{-2}$$
4. $$3.9\times 10^{8}~\text{Nm}^{-2}$$

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%
From NCERT
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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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