Q. No.The length of an elastic string is \(a\) metre when the longitudinal tension is \(4\) N and \(b\) metre when the longitudinal tension is \(5\) N. The length of the string in metre when the longitudinal tension is \(9\) N will be:
1.
\(a-b\)
2.
\(5b-4a\)
3.
\(2b-\frac{1}{4}a\)
4.
\(4a-3b\)
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A uniform cube is subjected to volume compression. If each side is decreased by 1%, then bulk strain is:
| 1. | 0.01 | 2. | 0.06 |
| 3. | 0.02 | 4. | 0.03 |
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A ball falling into a lake of depth 200 m shows a 0.1% decrease in its volume at the bottom. What is the bulk modulus of the material of the ball?
1.
2.
3.
4.
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If \(\mathrm{E}\) is the energy stored per unit volume in a wire having \(\mathrm{Y}\) as Young's modulus of the material, then the stress applied is:
1.
2.
3.
4.
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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 \(0.03\)%. |
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A uniform wire of length \(3\) m 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: (Take \(g=10\) ms-2)
| 1. | \(1.4 \times10^4\) N/m2 | 2. | \(4.8 \times10^3\) N/m2 |
| 3. | \(96 \times10^4\) N/m2 | 4. | \(3.5\times10^3\) N/m2 |
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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. |  |
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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 |
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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 |
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A metallic rope of diameter \(1~ \text{mm}\) breaks at \(10 ~\text{N}\) force. If the wire of the same material has a diameter of \(2~\text{mm}\), then the breaking force is:
| 1. | \(2.5~\text{N}\) | 2. | \(5~\text{N}\) |
| 3. | \(20~\text{N}\) | 4. | \(40~\text{N}\) |
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