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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%

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The density of metal at normal pressure is \(\rho\)$\mathrm{}$. lts density when it is subjected to an excess pressure \(P\) is \(\rho'\). lf \(B\) is the bulk modulus of the metal, the ratio \(\frac{ρ'}{\rho }\) is:

1. \(\frac{1}{1-\frac{p}{B}} \)

2. \(1+\frac{B}{P} \)

3. \(\frac{1}{1-\frac{B}{P}} \)

4. \(2+\frac{P}{B}\)

Subtopic: Shear and bulk modulus |

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The bulk modulus of rubber is \(9.8\times10^{8}~\text{N/m}^2\) To what depth a rubber ball be taken in a lake so that its volume is decreased by \(0.1\%\)?

1. | \(25\) m | 2. | \(100\) m |

3. | \(200\) m | 4. | \(500\) m |

Subtopic: Shear and bulk modulus |

87%

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If the ratio of lengths, radii and Young's modulus of steel and brass wires in the figure are \(a,\) \(b\) and \(c\) respectively, then the corresponding ratio of increase in their lengths will be:

1. | $\frac{2{a}^{2}c}{b}$ | 2. | $\frac{3a}{2{b}^{2}c}$ |

3. | $\frac{2ac}{{b}^{2}}$ | 4. | $\frac{3c}{2a{b}^{2}}$ |

Subtopic: Young's modulus |

84%

From NCERT

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A material has Poisson's ratio of \(0.5\). If a uniform rod made of it suffers a longitudinal strain of \(2\times 10^{-3}\), what is the percentage increase in volume?

1. \(2\%\)

2. \(4\%\)

3. \(0\%\)

4. \(5\%\)

Subtopic: Poisson's Ratio |

59%

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An elastic material of Young's modulus \(Y\) is subjected to a stress \(S\). The elastic energy stored per unit volume of the material is:

1. \(\frac{SY}{2}\)

2. \(\frac{S^2}{2Y}\)

3. \(\frac{S}{2Y}\)

4. \(\frac{2S}{Y}\)

Subtopic: Potential energy of wire |

90%

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lf \(\rho\) is the density of the material of a wire and \(\sigma\) is the breaking stress, the greatest length of the wire that can hang freely without breaking is:

1. \(\frac{2}{\rho g}\)

2. \(\frac{\rho}{\sigma g}\)

3. \(\frac{\rho g}{2 \sigma}\)

4. \(\frac{\sigma}{\rho g}\)

Subtopic: Stress - Strain |

73%

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The work done per unit volume to stretch the length of a wire by \(1\%\) with a constant cross-sectional area will be:

\(Y = 9\times10^{11}~\text{N/m}^2\)

1. \(9\times 10^{11}~\text{J}\)

2. \(4.5\times 10^{7}~\text{J}\)

3. \(9\times 10^{7}~\text{J}\)

4. \(4.5\times 10^{11}~\text{J}\)

Subtopic: Potential energy of wire |

73%

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A wire of length *\(L\)* and cross-sectional area *\(A\) *is made of a material of Young's modulus \(Y.\) It is stretched by an amount \(x.\) The work done is:

1. $\frac{YxA}{2L}$

2. $\frac{Y{x}^{2}A}{L}$

3. $\frac{Y{x}^{2}A}{2L}$

4. $\frac{2Y{x}^{2}A}{L}$

Subtopic: Potential energy of wire |

77%

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The Young's modulus of a wire is \(Y\). If the energy per unit volume is \(E\), then the strain will be:

1. \(\sqrt{\frac{2E}{Y}}\)

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

3. \(EY\)

4. \(\frac{E}{Y}\)

Subtopic: Potential energy of wire |

81%

From NCERT

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