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The average depth of the Indian Ocean is about \(3000\) m. The fractional compression, \(\dfrac{\Delta V}{V},\) of water at the bottom of the ocean is? (Given that the bulk modulus of water is \(2.2\times10^{9}\) Nm^{–2} and \(g=10\) ms^{–2})

1. \(1.36\times10^{-3}\)

2. \(2.36\times10^{-3}\)

3. \(1.36\times10^{-2}\)

4. \(2.36\times10^{-2}\)

Subtopic: Shear and bulk modulus |

73%

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A square lead slab of side \(50\) cm and thickness \(10\) cm is subject to a shearing force (on its narrow face) of \(9.0\times 10^{4}~\text{N}\)$\mathrm{}$. The lower edge is riveted to the floor as shown in the figure below. How much will the upper edge be displaced? (Shear modulus of lead \(= 5.6\times 10^{9}~\text{Nm}^{-2}\))

1. | \(0.16\) mm | 2. | \(1.8\) mm |

3. | \(18\) mm | 4. | \(16\) mm |

Subtopic: Shear and bulk modulus |

58%

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In a human pyramid in a circus, the entire weight of the balanced group is supported by the legs of a performer who is lying on his back (as shown in the figure below). The combined mass of all the persons performing the act, and the tables, plaques, etc. involved is \(280~\text{kg}\). The mass of the performer lying on his back at the bottom of the pyramid is \(60~\text{kg}\). Each thighbone (femur) of this performer has a length of \(50~\text{cm}\) and an effective radius of \(2.0~\text{cm}\). The amount by which each thighbone gets compressed under the extra load is: (The Young’s modulus for bone is given by, \(Y = 9.4\times 10^9~\text{N/m}^{2}\))

1. | \(4.55\times 10^{-5}~\text{cm}\) | 2. | \(5.45\times 10^{-3}~\text{cm}\) |

3. | \(5.45\times 10^{-5}~\text{cm}\) | 4. | \(4.55\times 10^{-3}~\text{cm}\) |

Subtopic: Stress - Strain |

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A copper wire of length \(2.2\) m and a steel wire of length \(1.6\) m, both of diameter \(3.0\) mm, are connected end to end. When stretched by a load, the net elongation is found to be \(0.70\) mm. The load applied is: \(Y_C = 1.1\times 10^{11}~\text{Nm}^{-2}~\text{and}~Y_S = 2.0\times 10^{11}~\text{Nm}^{-2}\)

1. \(1.8\times 10^{2}~\text{N}\)

2. \(1.8~\text{N}\)

3. \(1.8\times 10^{3}~\text{N}\)

4. \(18\times 10^{3}~\text{N}\)

1. \(1.8\times 10^{2}~\text{N}\)

2. \(1.8~\text{N}\)

3. \(1.8\times 10^{3}~\text{N}\)

4. \(18\times 10^{3}~\text{N}\)

Subtopic: Hooke's Law |

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A structural steel rod has a radius of \(10~\text{mm}\) and a length of \(1.0~\text{m}.\) A \(100~\text{kN}\) force stretches it along its length. The stress produced and the elongation in the rod, respectively, are?

(Young’s modulus of structural steel is \(2.0\times 10^{11}~\text{Nm}^{-2}.)\)

1. \(3.18\times 10^{7}~\text{Nm}^{-2}~\text{and}~2.59~\text{mm}\)

2. \(3.18\times 10^{8}~\text{Nm}^{-2}~\text{and}~1.59~\text{m}\)

3. \(3.18\times 10^{8}~\text{Nm}^{-2}~\text{and}~1.59~\text{mm}\)

4. \(3.18\times 10^{7}~\text{Nm}^{-2}~\text{and}~2.59~\text{m}\)

(Young’s modulus of structural steel is \(2.0\times 10^{11}~\text{Nm}^{-2}.)\)

1. \(3.18\times 10^{7}~\text{Nm}^{-2}~\text{and}~2.59~\text{mm}\)

2. \(3.18\times 10^{8}~\text{Nm}^{-2}~\text{and}~1.59~\text{m}\)

3. \(3.18\times 10^{8}~\text{Nm}^{-2}~\text{and}~1.59~\text{mm}\)

4. \(3.18\times 10^{7}~\text{Nm}^{-2}~\text{and}~2.59~\text{m}\)

Subtopic: Hooke's Law |

68%

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