Q. No.A light rod of length 2m is suspended from the ceiling horizontally by means of two vertical wires of equal length. A weight W is hung from the light rod as shown in the figure. The rod is hung by means of a steel wire of cross-sectional area and brass wire of cross-sectional area . To have equal stress in both wires, =?
1.
1/3
2.
1/4
3.
4/3
4.
1/2
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A vessel of \(1\times 10^{-3}\) m3 volume contains oil. When a pressure of \(1.2 \times10^5\) N/m2 is applied on it, then volume decreases by \(0.3 \times 10^{-6}\) m3. The bulk modulus of oil is:
| 1. | \(1 \times 10^6 \mathrm{~N} / \mathrm{m}^2 \) | 2. | \(2 \times 10^7 \mathrm{~N} / \mathrm{m}^2 \) |
| 3. | \(4 \times 10^8 \mathrm{~N} / \mathrm{m}^2 \) | 4. | \(6 \times 10^{10} \mathrm{~N} / \mathrm{m}^2\) |
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The stress-strain curves are drawn for two different materials \(X\) and \(Y.\) It is observed that the ultimate strength point and the fracture point are close to each other for material \(X\) but are far apart for material \(Y.\) We can say that the materials \(X\) and \(Y\) are likely to be (respectively):
| 1. | ductile and brittle |
| 2. | brittle and ductile |
| 3. | brittle and plastic |
| 4. | plastic and ductile |
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A steel ring of radius \(\mathrm{r}\) and cross-section area \(\mathrm{A}\) is fitted onto a wooden disc of radius \(\mathrm{R}(\mathrm{R}>\mathrm{r}).\) If Young's modulus is \(\mathrm{E},\) then the force with which the steel ring is expanded is:
| 1. | \(\mathrm{AE} \frac{\mathrm{R}}{\mathrm{r}} \) | 2. | \(A E \frac{R-r}{r} \) |
| 3. | \(\frac{E}{A} \frac{R-r}{A} \) | 4. | \(\frac{\mathrm{Er}}{\mathrm{AR}}\) |
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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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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 |
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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. \(\Delta l ~\text{vs}~l\)
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