A uniform wire of length 3m and mass 10 kg is suspended vertically from one end and loaded at another end by a block of mass 10 kg. The radius of the cross-section of the wire is 0.1 m. The stress in the middle of the wire is: (g = 10 ${\mathrm{ms}}^{-2}$)

1. 1.4 x ${10}^{4}\mathrm{N}/{\mathrm{m}}^{2}$

2. 4.8 x ${10}^{3}\mathrm{N}/{\mathrm{m}}^{2}$

3. 96 x ${10}^{4}\mathrm{N}/{\mathrm{m}}^{2}$

4. 3.5 x ${10}^{3}\mathrm{N}/{\mathrm{m}}^{2}$

67%

Subtopic: Stress - Strain |

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A uniform wire is held at one end and stretched by applying force at the other end. If the product of the length of wire and area of cross-section of the wire remains unchanged, then Poisson's ratio of material of the wire will be:

1. 0

2. 0.50

3. -0.5

4. Infinity

Subtopic: Poisson's Ratio |

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The elongation (x) of a steel wire varies with the elongating force (F) according to the graph: (within elastic limit)

1. | 2. | ||

3. | 4. |

Subtopic: Stress - Strain Curve |

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The stress-strain curve for two materials A and B are as shown in the figure. Select the correct statement-

1. Material A is less brittle and less elastic as compared to B

2. Material A is more ductile and less elastic as compared to B

3. Material A is less brittle and more elastic than B

4. Material B is more brittle and more elastic than A

Subtopic: Stress - Strain Curve |

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The Young's modulus of a wire is numerically equal to the stress at a point when:

1. the strain produced in the wire is equal to unity.

2. the length of the wire gets doubled.

3. the length increases by 100%.

4. All of these

Subtopic: Young's modulus |

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Two wires X and Y of the same length are made of the same material. The figure represents the load F versus extension $\u2206\mathrm{x}$ graph for the two wires. Hence:

1. Modulus of elasticity of Y is greater than that of X.

2. Stiffness of Y is more than that of X.

3. The cross-sectional area of Y is less than that of X.

4. All of these

From NCERT

Subtopic: Stress - Strain Curve |

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A metallic rope of diameter 1 mm breaks at 10 N force. If the wire of the same material has a diameter of 2 mm, then the breaking force is:

1. 2.5 N

2. 5 N

3. 20 N

4. 40 N

Subtopic: Young's modulus |

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The Poisson's ratio of a material is 0.4. If a force is applied to a wire of this material, there is a decrease in the cross-section area by 2%. In such a case the percentage increase in its length will be:

1. 3%

2. 2.5%

3. 1%

4. 0.5%

Subtopic: Poisson's Ratio |

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The breaking stress of a wire going over a smooth pulley in the following question is 2 × ${10}^{9}$ N/${\mathrm{m}}^{2}$. What would be the minimum radius of the wire used if it is not to break?

1. $0.46\times {10}^{-6}\mathrm{m}$

2. $0.46\times {10}^{-4}\mathrm{m}$

3. $0.46\times {10}^{8}\mathrm{m}$

4. $0.46\times {10}^{-11}\mathrm{m}$

Subtopic: Stress - Strain |

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The increase in the length of a wire on stretching is 0.04%. If Poisson's ratio for the material of wire is 0.5, then the diameter of the wire will:

1. decrease by 0.02%.

2. decrease by 0.01%.

3. decrease by 0.04%.

4. increase by 0.03%.

Subtopic: Poisson's Ratio |

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