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The stress-strain curves are drawn for two different materials \(X\) and \(Y.\) It is observed that the ultimate strength point and the fracture point are close to each other for material \(X\) but are far apart for material \(Y.\) We can say that the materials \(X\) and \(Y\) are likely to be (respectively):

1. | ductile and brittle |

2. | brittle and ductile |

3. | brittle and plastic |

4. | plastic and ductile |

Subtopic: Stress - Strain Curve |

81%

From NCERT

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A vessel of \(1\times 10^{-3}\) m^{3} volume contains oil. When a pressure of \(1.2 \times10^5\) N/m^{2 }is applied on it, then volume decreases by \(0.3 \times 10^{-6}\) m^{3}. The bulk modulus of oil is:

1. | \(1 \times 10^6~\text{N/m}^2\) | 2. | \(2 \times 10^7~\text{N/m}^2\) |

3. | \(4 \times 10^8~\text{N/m}^2\) | 4. | \(6 \times 10^{10}~\text{N/m}^2\) |

Subtopic: Shear and bulk modulus |

86%

From NCERT

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A wire of negligible mass and length \(2\) m is stretched by hanging a \(20\) kg load to its lower end keeping its upper end fixed. If work done in stretching the wire is \(50\) J, then the strain produced in the wire will be:

1. \(0.5\)

2. \(0.1\)

3. \(0.4\)

4. \(0.25\)

Subtopic: Potential energy of wire |

63%

From NCERT

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The length of an elastic string is \(a\) metre when the longitudinal tension is \(4\) N and \(b\) metre when the longitudinal tension is \(5\) N. The length of the string in metre when the longitudinal tension is \(9\) N will be:

1. | \(a-b\) | 2. | \(5b-4a\) |

3. | \(2b-\frac{1}{4}a\) | 4. | \(4a-3b\) |

Subtopic: Hooke's Law |

76%

From NCERT

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The compressibility of water is \(4\times 10^{-5}\) per unit atmospheric pressure. The decrease in volume of \(100\) cubic centimeter of water under a pressure of \(100\) atmosphere will be:

1. \(0.4~\text{cc}\)

2. \(4\times 10^{-5}~\text{cc}\)

3. \(0.025~\text{cc}\)

4. \(0.004~\text{cc}\)

Subtopic: Shear and bulk modulus |

63%

From NCERT

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A uniform cube is subjected to volume compression. If each side is decreased by \(1\%\), then bulk strain is:

1. | \(0.01\) | 2. | \(0.06\) |

3. | \(0.02\) | 4. | \(0.03\) |

Subtopic: Shear and bulk modulus |

65%

From NCERT

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A ball falling into a lake of depth \(200~\text{m}\) shows a \(0.1\%\) decrease in its volume at the bottom. What is the bulk modulus of the material of the ball?

1. \(19.6\times 10^{8}~\text{N/m}^2\)

2. \(19.6\times 10^{-10}~\text{N/m}^2\)

3. \(19.6\times 10^{10}~\text{N/m}^2\)

4. \(19.6\times 10^{-8}~\text{N/m}^2\)

Subtopic: Shear and bulk modulus |

82%

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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 |

77%

From NCERT

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If \(E\) is the energy stored per unit volume in a wire having \(Y\) as Young's modulus of the material, then the stress applied is:

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

2. \(2\sqrt{EY}\)

3. \(\frac{1}{2}\sqrt{EY}\)

4. \(\frac{3}{2}\sqrt{EY}\)

Subtopic: Potential energy of wire |

85%

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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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