# lf $\mathrm{\rho }$ is the density of the material of a wire and $\sigma$ is the breaking stress, the greatest length of the wire that can hang freely without breaking is: 1.$\frac{2}{\mathrm{\rho g}}$ 2. $\frac{\mathrm{\rho }}{\mathrm{\sigma g}}$ 3.$\frac{\mathrm{\rho g}}{2\mathrm{\sigma }}$ 4. $\frac{\mathrm{\sigma }}{\mathrm{\rho g}}$

Subtopic:  Stress - Strain |
72%
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An elastic material of Young's modulus Y is subjected to a stress S. The elastic energy stored per unit volume of the material is:

1. $\frac{SY}{2}$  

2. $\frac{{S}^{2}}{2Y}$

3. $\frac{S}{2Y}$ 

4. $\frac{2S}{Y}$

Subtopic:  Potential energy of wire |
90%
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A material has Poisson's ratio of 0.5. If a uniform rod made of it suffers a longitudinal strain of $2×{10}^{-3}$, what is the percentage increase in volume?

1.  2%

2.  4%

3.  0%

4.  5%

Subtopic:  Poisson's Ratio |
59%
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If the ratio of lengths, radii and Young's modulus of steel and brass wires in the figure are $$a,$$ $$b$$ and $$c$$ respectively, then the corresponding ratio of increase in their lengths will be:

1. $\frac{2{a}^{2}c}{b}$

2. $\frac{3a}{2{b}^{2}c}$

3. $\frac{2ac}{{b}^{2}}$

4. $\frac{3c}{2a{b}^{2}}$

Subtopic:  Young's modulus |
83%
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The bulk modulus of rubber is . To what depth a rubber ball be taken in a lake so that its volume is decreased by 0.1%?

 1 25 m 2 100 m 3 200 m 4 500 m
Subtopic:  Shear and bulk modulus |
87%
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The density of metal at normal pressure is $\mathrm{\rho }$. lts density when it is subjected to an excess pressure P is $\mathrm{\rho }$'. lf B is the bulk modulus of the metal, the ratio $\frac{\mathrm{\rho \text{'}}}{\mathrm{\rho }}$ is:
1. $$\frac{1}{1-\frac{p}{B}}$$
2. $$1+\frac{B}{P}$$
3. $$\frac{1}{1-\frac{B}{P}}$$
4. $$2+\frac{P}{B}$$

Subtopic:  Shear and bulk modulus |
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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%
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The work done per unit volume to stretch the length of a wire by 1%  with a constant cross-sectional area will be: $\left[Y=9×{10}^{11}N/{m}^{2}\right]$

1. $9×{10}^{11}$ $J$

2. $4.5×{10}^{7}J$

3. $9×{10}^{7}J$

4. $4.5×{10}^{11}$ $J$

Subtopic:  Potential energy of wire |
73%
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A wire of length $$L$$ and cross-sectional area $$A$$ is made of a material of Young's modulus $$Y.$$ It is stretched by an amount $$x.$$ The work done is:
1. $\frac{YxA}{2L}$

2. $\frac{Y{x}^{2}A}{L}$

3. $\frac{Y{x}^{2}A}{2L}$

4. $\frac{2Y{x}^{2}A}{L}$

Subtopic:  Potential energy of wire |
77%
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The Young's modulus of a wire is Y.  If the energy per unit volume is E, then the strain will be:

1. $\sqrt{\frac{2E}{Y}}$

2. $\sqrt{2EY}$

3. $EY$

4. $\frac{E}{Y}$

Subtopic:  Potential energy of wire |
81%
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