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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 |

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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%

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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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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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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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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%

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A steel ring of radius \(r\) and cross-section area \(A\) is fitted onto a wooden disc of radius \(R(R>r).\) If Young's modulus is \({E},\) then the force with which the steel ring is expanded is:

1. | \({AE} \frac{R}{r} \) | 2. | \(A E \left(\frac{R-r}{r}\right)\) |

3. | \(\frac{E}{A}\left(\frac{R-r}{A}\right)\) | 4. | \(\frac{Er}{AR}\) |

Subtopic: Young's modulus |

85%

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A light rod of length \(2~\text{m}\) is suspended from the ceiling horizontally by means of two vertical wires of equal length. A weight \(W\) is hung from the light rod as shown in the figure. The rod is hung by means of a steel wire of cross-sectional area \(A_1 = 0.1~\text{cm}^2\) and brass wire of cross-sectional area\(A_2 = 0.2~\text{cm}^2\). To have equal stress in both wires, \(\frac{T_1}{T_2}?\)${\mathrm{}}_{}$

1. | \(1/3\) | 2. | \(1/4\) |

3. | \(4/3\) | 4. | \(1/2\) |

Subtopic: Stress - Strain |

75%

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The stress versus strain graphs for wires of two materials \(A\) and \(B\) are as shown in the figure. If \(Y_A\) $\mathrm{and}$ \(Y_B\) are the Young's moduli of the materials, then:

1. | \(Y_B = 2Y_A\) | 2. | \(Y_A = Y_B\) |

3. | \(Y_B = 3Y_A\) | 4. | \(Y_A =3 Y_B\) |

Subtopic: Stress - Strain Curve |

77%

From NCERT

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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 |

71%

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