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

1. | \(\times\)strain | stress

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 |

90%

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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 |

86%

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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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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 |

80%

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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 |

78%

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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 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: $\left[Y=9\times {10}^{11}N/{m}^{2}\right]$

1. $9\times {10}^{11}$ $J$

2. $4.5\times {10}^{7}J$

3. $9\times {10}^{7}J$

4. $4.5\times {10}^{11}$ $J$

Subtopic: Potential energy of wire |

73%

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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 |

70%

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