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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 3L/4 from its lower end is:

1. $\frac{\mathrm{W}+{\mathrm{W}}_{1}}{\mathrm{A}}$

2. $\frac{4\mathrm{W}+{\mathrm{W}}_{1}}{3\mathrm{A}}$

3. $\frac{3\mathrm{W}+{\mathrm{W}}_{1}}{4\mathrm{A}}$

4. $\frac{{\displaystyle \frac{3}{4}}\mathrm{W}+{\mathrm{W}}_{1}}{\mathrm{A}}$

Subtopic: Stress - Strain |

70%

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

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

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

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

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

Subtopic: Shear and bulk modulus |

84%

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To break a wire, a force of ${10}^{6}$ $N/{m}^{2}$ is required. If the density of the material is $3\times {10}^{3}$ $kg/{m}^{3}$, 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 4N, and ${l}_{2}$ metres when the tension is 5N. The length in metres when the tension is 0 N will be:

1. $5{l}_{1}-4{l}_{2}$

2. $5{l}_{2}-4{l}_{1}$

3. $9{l}_{1}-8{l}_{2}$

4. $9{l}_{2}-8{l}_{1}$

Subtopic: Hooke's Law |

63%

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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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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: ($\mathrm{Y}=2.0\times {10}^{11}$ ${\mathrm{Nm}}^{-2}$)

1. $3.2\times {10}^{11}$ ${\mathrm{Nm}}^{-2}$

2. $3.2\times {10}^{7}$ ${\mathrm{Nm}}^{-2}$

3. $3.6\times {10}^{9}$ ${\mathrm{Nm}}^{-2}$

4. 3.9$\times {10}^{8}$ ${\mathrm{Nm}}^{-2}$

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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A uniform cylinder rod of length L, cross-sectional area A and Young's modulus Y is acted upon by the forces, as shown in the figure. The elongation of the rod is:

1. | $\frac{3FL}{5AY}$ | 2. | $\frac{2FL}{5AY}$ |

3. | $\frac{2FL}{8AY}$ | 4. | $\frac{8FL}{3AY}$ |

Subtopic: Young's modulus |

57%

From NCERT

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