Q. No.The average depth of the Indian Ocean is about \(3000~\text m.\) The fractional compression \(\frac{\Delta V}{V},\) of water at the bottom of the ocean is?
(Given that the bulk modulus of water is \(2.2\times10^{9}~\text{Nm}^{-2}\) and \(g=10~\text{ms}^{-2}\))
1. \(1.36\times10^{-3}\)
2. \(2.36\times10^{-3}\)
3. \(1.36\times10^{-2}\)
4. \(2.36\times10^{-2}\)
(Given that the bulk modulus of water is \(2.2\times10^{9}~\text{Nm}^{-2}\) and \(g=10~\text{ms}^{-2}\))
1. \(1.36\times10^{-3}\)
2. \(2.36\times10^{-3}\)
3. \(1.36\times10^{-2}\)
4. \(2.36\times10^{-2}\)
The figure given below shows the longitudinal stress vs longitudinal strain graph for a given material. Based on the given graph, Young's modulus of the material with the increase in strain will:
1. be variable.
2. first increase & then decrease.
3. first decrease & then increase.
4. remain constant.
A square lead slab of side \(50~\text{cm}\) and thickness \(10~\text{cm}\) is subject to a shearing force (on its narrow face) of \(9.0\times 10^{4}~\text{N}.\) 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. | \(0.16~\text{mm}\) | 2. | \(1.8~\text{mm}\) |
| 3. | \(18~\text{mm}\) | 4. | \(16~\text{mm}\) |
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. | \(4.55\times 10^{-3}~\text{cm}\) |
1. \(1.8\times 10^{2}~\text{N}\)
2. \(1.8~\text{N}\)
3. \(1.8\times 10^{3}~\text{N}\)
4. \(18\times 10^{3}~\text{N}\)
(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. \(3.18\times 10^{7}~\text{Nm}^{-2}~\text{and}~2.59~\text{m}\)
| (a) | the same stress | (b) | different stress |
| (c) | the same strain | (d) | different strain |
Choose the correct option:
| 1. | (a), (b) | 2. | (a), (d) |
| 3. | (b), (c) | 4. | (c), (d) |
| (a) | The bulk modulus is infinite. |
| (b) | The bulk modulus is zero. |
| (c) | The shear modulus is infinite. |
| (d) | The shear modulus is zero. |
Choose the correct option from the options given below:
| 1. | (a) and (d) only |
| 2. | (b) and (d) only |
| 3. | (b) and (c) only |
| 4. | (c) and (d) only |
\((Y_{\text{Al}}=70\times10^9~\text{N/m}^2\) and \(Y_{\text{steel}}=200\times10^9~\text{N/m}^2)\)
| (a) | The mass \(m\) should be suspended close to wire \(A\) to have equal stresses in both wires. |
| (b) | The mass \(m\) should be suspended close to \(B\) to have equal stresses in both wires. |
| (c) | The mass \(m\) should be suspended in the middle of the wires to have equal stresses in both wires. |
| (d) | The mass \(m\) should be suspended close to wire \(A\) to have equal strain in both wires. |
The correct statements are:
| 1. | (b), (c) | 3. | (b), (d) |
| 2. | (a), (d) | 4. | (c), (d) |
A wire is suspended from the ceiling and stretched under the action of a weight \(F\) suspended from its other end. The force exerted by the ceiling on it is equal and opposite to the weight.
| (a) | Tensile stress at any cross-section \(A\) of the wire is \(F/A.\) |
| (b) | Tensile stress at any cross-section is zero. |
| (c) | Tensile stress at any cross-section \(A\) of the wire is \(2F/A.\) |
| (d) | Tension at any cross-section \(A\) of the wire is \(F.\) |
Choose the correct option from the given ones:
1. (a) and (b) only
2. (a) and (d) only
3. (b) and (c) only
4. (a) and (c) only
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