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Copper of fixed volume \(V\) is drawn into a wire of length \(l.\) When this wire is subjected to a constant force \(F,\) the extension produced in the wire is \(\Delta l.\) Which of the following graphs is a straight line?

1. \(\Delta l ~\text{vs}~\frac{1}{l}\)

2. \(\Delta l ~\text{vs}~l^2\)

3. \(\Delta l ~\text{vs}~\frac{1}{l^2}\)

4. \(\Delta l ~\text{vs}~l\)

Subtopic: Young's modulus |

70%

From NCERT

AIPMT - 2014

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Overall changes in volume and radius of a uniform cylindrical steel wire are \(0.2\%\) and \(0.002\%\) respectively when subjected to some suitable force. Longitudinal tensile stress acting on the wire is: \(\left(2.0\times 10^{11}~\text{Nm}^{-2}\right)\)

1. \(3.2\times 10^{11}~\text{Nm}^{-2}\)

2. \(3.2\times 10^{7}~\text{Nm}^{-2}\)

3. \(3.6\times 10^{9}~\text{Nm}^{-2}\)

4. \(3.9\times 10^{8}~\text{Nm}^{-2}\)

Subtopic: Young's modulus |

From NCERT

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A 1000 kg lift is tied with metallic wires of maximum safe stress of 1.4 $\times $ 10^{8} N m^{-2}. If the maximum acceleration of the lift is 1.2 m s^{-2}, then the minimum diameter of the wire is:

1. 1 m

2. 0.1 m

3. 0.01 m

4. 0.001 m

Subtopic: Stress - Strain |

55%

From NCERT

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A wire can sustain a weight of 10 kg before breaking. If the wire is cut into two equal parts, then each part can sustain a weight of:

1. | 2.5 kg | 2. | 5 kg |

3. | 10 kg | 4. | 15 kg |

Subtopic: Stress - Strain |

72%

From NCERT

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Two wires are made of the same material and have the same volume. The first wire has a cross-sectional area \(A\) and the second wire has a cross-sectional area \(3A\). If the length of the first wire is increased by \(\Delta l\) on applying a force \(F\), how much force is needed to stretch the second wire by the same amount?

1. | \(9F\) | 2. | \(6F\) |

3. | \(4F\) | 4. | \(F\) |

Subtopic: Young's modulus |

76%

From NCERT

NEET - 2018

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One end of a uniform wire of length \(L\) and of weight \(W\) is attached rigidly to a point in the roof and a weight \(W_1\) is suspended from its lower end. If \(A\) is the area of cross-section of the wire, the stress in the wire at a height \(\frac{3L}{4}\) from its lower end is:

1. \(\frac{W+W_1}{A}\)

2. \(\frac{4W+W_1}{3A}\)

3. \(\frac{3W+W_1}{4A}\)

4. \(\frac{\frac{3}{4}W+W_1}{A}\)

Subtopic: Stress - Strain |

70%

From NCERT

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The bulk modulus of water is \(2\times 10^{9}~\text{N/m}^2\)${\mathrm{}}^{}$. The increase in pressure required to decrease the volume of water sample by \(0.1\%\) is:

1. \(4 \times 10^{6}~\text{N/m}^2\)

2. \(2 \times 10^{6}~\text{N/m}^2\)

3. \(2 \times 10^{8}~\text{N/m}^2\)

4. \(8 \times 10^{6}~\text{N/m}^2\)

Subtopic: Shear and bulk modulus |

84%

From NCERT

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Choose the correct statement.

1. | Breaking stress does not depend on the area of cross-section. |

2. | \(B_{\text {solid }}>{B}_{\text {gas }}>{B}_{\text {liquid }}\) where \(B\) is the bulk modulus. |

3. | Breaking load does not depend on the area of cross-section. |

4. | Young's modulus always decreases on decreasing the temperature. |

Subtopic: Shear and bulk modulus |

54%

From NCERT

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To break a wire, a force of \(10^6~\text{N/m}^{2}\) is required. If the density of the material is \(3\times 10^{3}~\text{kg/m}^3,\) then the length of the wire which will break by its own weight will be:

1. \(34\) m

2. \(30\) m

3. \(300\) m

4. \(3\) m

Subtopic: Stress - Strain |

61%

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The length of elastic string, obeying Hooke's law is \(l_1\) metres when the tension is \(4~\text{N}\), and \(l_2\) metres when the tension is \(5~\text{N}\). The length in metres when the tension is \(0~\text{N}\) will be:

1. \(5l_1-4l_2\)

2. \(5l_2-4l_1\)

3. \(9l_1-8l_2\)

4. \(9l_2-8l_1\)

Subtopic: Hooke's Law |

63%

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