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Q. No.The elastic energy stored in a wire of Young's Modulus \(Y\) is:
1. \(Y \times \dfrac{\left(\text{strain}\right)^{2}}{\text{volume}}\)
2. \(\text{stress} \times \text{strain} \times \text{volume}\)
3. \(\dfrac{\left(\text{strain}\right)^{2} \times \text{volume}}{2 Y}\)
4. \(\dfrac{1}{2} \times \text{stress} \times \text{strain} \times \text{volume}\)
Subtopic: Potential energy of wire |
90%
Level 1: 80%+
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A wire of natural length \(L\) and cross-sectional area \(A\) is made of a material of Young’s modulus \(Y.\) If the wire is stretched by an amount \(x,\) the energy stored in the wire is:
| 1. | \( \dfrac{Y A x^{2}}{L}\) | 2. | \( \dfrac{Y A x^{2}}{2 L}\) |
| 3. | \(\dfrac{2 Y A x^{2}}{L}\) | 4. | \(\dfrac{Y A x^{2}}{L^{2}}\) |
Subtopic: Potential energy of wire |
89%
Level 1: 80%+
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The energy density in a wire which is under stress is given by:
| 1. | \({\Large\frac12}\text{(stress)}^2 \) | 2. | \({\Large\frac12}\text{(strain)}^2\) |
| 3. | \({\Large\frac12}\text{(stress)}\times\text{(strain)}\) | 4. | \({\Large\frac{1}{2}\frac{\text{(stress)}^2}{\text{strain}}}\) |
Subtopic: Potential energy of wire |
87%
Level 1: 80%+
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Given below are two statements:
| Assertion (A): | Identical springs of steel and copper are equally stretched. More work will be done on the steel spring. |
| Reason (R): | Steel is more elastic than copper. |
| 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. | Both (A) and (R) are False. |
Subtopic: Potential energy of wire |
86%
Level 1: 80%+
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A wire of length \(L\) and cross-sectional area \(A\) is made of a material of Young’s modulus \(Y.\) On stretching the length of the wire by \(l,\) the elastic energy stored per unit volume is:
| 1. | \(\dfrac{FA}{2L}\) | 2. | \(\dfrac{Fl}{2AL}\) |
| 3. | \(\dfrac{Fl}{AL}\) | 4. | \(\dfrac{FL}{Al}\) |
Subtopic: Potential energy of wire |
84%
Level 1: 80%+
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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. \(\sqrt{\dfrac{2 E}{Y}} \)
2. \(\sqrt{2 E Y}\)
3. \(E Y\)
4. \(\dfrac{E}{Y}\)
Subtopic: Potential energy of wire |
83%
Level 1: 80%+
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When a rubber is stretched, what happens to its energy?
| 1. | Its kinetic energy increases. |
| 2. | Its potential energy increases. |
| 3. | Its kinetic energy decreases. |
| 4. | Its potential energy decreases. |
Subtopic: Potential energy of wire |
80%
Level 1: 80%+
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Work done by the restoring force in a wire within its elastic limit is \(-10~\text{J}\). The maximum amount of heat produced in the wire is:
1. \(10~\text{J}\)
2. \(20~\text{J}\)
3. \(5~\text{J}\)
4. \(15~\text{J}\)
1. \(10~\text{J}\)
2. \(20~\text{J}\)
3. \(5~\text{J}\)
4. \(15~\text{J}\)
Subtopic: Potential energy of wire |
79%
Level 2: 60%+
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