# 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 |
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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 $$2\times 10^{-3}$$, what is the percentage increase in volume?
1. $$2\%$$
2. $$4\%$$
3. $$0\%$$
4. $$5\%$$

Subtopic:  Poisson's Ratio |
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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 |
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The bulk modulus of rubber is $$9.8\times10^{8}~\text{N/m}^2$$ 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 |
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The density of metal at normal pressure is $$\rho$$$\mathrm{}$. lts density when it is subjected to an excess pressure $$P$$ is $$\rho'$$. lf $$B$$ is the bulk modulus of the metal, the ratio $$\frac{ρ'}{\rho }$$ 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 |
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lf $$\rho$$ 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. $$\frac{2}{\rho g}$$
2. $$\frac{\rho}{\sigma g}$$
3. $$\frac{\rho g}{2 \sigma}$$
4. $$\frac{\sigma}{\rho g}$$

Subtopic:  Stress - Strain |
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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:
$$Y = 9\times10^{11}~\text{N/m}^2$$
1. $$9\times 10^{11}~\text{J}$$
2. $$4.5\times 10^{7}~\text{J}$$
3. $$9\times 10^{7}~\text{J}$$
4. $$4.5\times 10^{11}~\text{J}$$

Subtopic:  Potential energy of wire |
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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 |
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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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