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The length of a metal wire is \(l_1\) when the tension in it is \(T_1\) and is \(l_2\) when the tension is \(T_2.\) The natural length of the wire is:

1. \(\frac{l_{1}+l_{2}}{2}\)

2. \(\sqrt{l_{1} l_{2}}\)

3. \(\frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}}\)

4. \(\frac{l_{1} T_{2}+l_{2} T_{1}}{T_{2}+T_{1}}\)

Subtopic: Â Young's modulus |

Â 66%

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A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break:

1. | when the mass is at the highest point |

2. | when the mass is at the lowest point |

3. | when the wire is horizontal |

4. | at an angle of \(\cos^{-1}(\frac{1}{3})\) from the upward vertical |

Subtopic: Â Stress - Strain |

Â 73%

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When a metal wire elongates by hanging a load on it, the gravitational potential energy is decreased.

1. | this energy completely appears as the increased kinetic energy of the block |

2. | this energy completely appears as the increased elastic potential energy of the wire |

3. | this energy completely appears as heat |

4. | none of these |

Subtopic: Â Potential energy of wire |

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The dimension \([ML^{-1}T^{-2}]\) can correspond to:

1. | moment of a force |

2. | surface tension |

3. | modulus of elasticity |

4. | coefficient of viscosity |

Subtopic: Â Young's modulus |

Â 79%

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A student plots a graph from his readings on the determination of Young modulus of a metal wire but forgets to put the labels (figure). The quantities on X and Y-axes may be respectively,

(a) | weight hung and length increased |

(b) | stress applied and length increased |

(c) | stress applied and strain developed |

(d) | length increased and the weight hung |

Choose the correct option:

1. | (a) and (b) |

2. | (b) and (c) |

3. | (a), (b) and (d) |

4. | all of these |

Subtopic: Â Young's modulus |

Â 57%

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When a metal wire is stretched by a load, the fractional change in its volume \(\frac{\Delta V}{V}\) is proportional to:

1. \(\frac{\Delta l}{l}\)

2. \(\left(\frac{\Delta l}{l}\right)^{2}\)

3. \(\sqrt{\Delta l/ l}\)

4. none of these

Subtopic: Â Poisson's Ratio |

Â 55%

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A heavy uniform rod is hanging vertically from a fixed support. It is stretched by its own weight. The diameter of the rod is:

1. | smallest at the top and gradually increases down the rod. |

2. | largest at the top and gradually decreases down the rod. |

3. | uniform everywhere. |

4. | maximum in the middle. |

Subtopic: Â Stress - Strain |

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A wire elongates by \(1.0\) mm when a load \(W\) is hang from it. If this wire goes over a pulley and two weights \(W\) each are hung at the two ends, the elongation of the wire will be:

1. \(0.5\) m

2. \(1.0\) mm

3. \(2.0\) mm

4. \(4.0\) mm

Subtopic: Â Young's modulus |

Â 65%

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Two wires \(A\) and \(B\) are made of same material. The wire \(A\) has a length \(L\) and diameter \(r\) while the wire \(B\) has a length \(2L\) and diameter \(r/2.\) If the two wires are stretched by the same force, the elongation in \(A\) divided by the elongation in \(B\) is:

1. \(\frac{1}{8}\)

2. \(\frac{1}{4}\)

3. \(4\)

4. \(8\)

Subtopic: Â Young's modulus |

Â 77%

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A wire can sustain a weight of \(20\) kg before breaking. If the wire is cut into two equal parts, each part can sustain a weight of:

1. | \(10\) kg | 2. | \(20\) kg |

3. | \(40\) kg | 4. | \(80\) kg |

Subtopic: Â Stress - Strain |

Â 72%

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