The work done in stretching an elastic wire per unit volume is:

 1 stress$$\times$$strain 2 $$\frac{1}{2}$$ $$\times$$ stress$$\times$$strain 3 $$2\times$$ stress$$\times$$strain 4 stress/strain
Subtopic:  Potential energy of wire |
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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 |
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If $$\mathrm{E}$$ is the energy stored per unit volume in a wire having $$\mathrm{Y}$$ as Young's modulus of the material, then the stress applied is:
1. $\sqrt{2\mathrm{EY}}$

2. $2\sqrt{\mathrm{EY}}$

3. $\frac{1}{2}\sqrt{\mathrm{EY}}$

4. $\frac{3}{2}\sqrt{\mathrm{EY}}$

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 |
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Given below are two statements:
 Assertion (A): Soft steel can be made red hot by continued hammering on it, but hard steel cannot. Reason (R): Energy transfer in the case of soft is large as in hard steel.

 1 Both (A) and (R) are True and (R) is the correct explanation of (A). 2 Both (A) and (R) are True but (R) is not the correct explanation of (A). 3 (A) is True but (R) is False. 4 (A) is False but (R) is True.
Subtopic:  Potential energy of wire |
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A $$5$$ m long wire is fixed to the ceiling. A weight of $$10$$ kg is hung at the lower end and is $$1$$ m above the floor. The wire was elongated by $$1$$ mm. The energy stored in the wire due to stretching is:
1. zero
2. $$0.05$$ J
3. $$100$$ J
4. $$500$$ 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 ratio of Young's modulus of the material of two wires is 2 : 3. If the same stress is applied on both, then the ratio of elastic energy per unit volume will be:

1. 3 : 2

2. 2 : 3

3. 3 : 4

4. 4 : 3

Subtopic:  Potential energy of wire |
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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 |
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If the force constant of a wire is K, the work done in increasing the length of the wire by l is:

1. $Kl/2$

2. $Kl$

3. $K{l}^{2}/2$

4. $K{l}^{2}$

Subtopic:  Potential energy of wire |
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