Q. No.The breaking stress of a wire depends upon:
1.
material of the wire.
2.
length of the wire.
3.
radius of the wire.
4.
shape of the cross-section.
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Three wires \(A,B,C\) made of the same material and radius have different lengths. The graphs in the figure show the elongation-load variation. The longest wire is:
1. \(A\)
2. \(B\)
3. \(C\)
4. All of the above
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| 1. | \(1:2\) | 2. | \(2:1\) |
| 3. | \(4:1\) | 4. | \(1:1\) |
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The area of cross-section of a wire of length \(1.1\) m is \(1\) mm2. It is loaded with mass of \(1\) kg. If Young's modulus of copper is \(1.1\times10^{11}\) N/m2, then the increase in length will be: (If \(g = 10~\text{m/s}^2)\)
| 1. | \(0.01\) mm | 2. | \(0.075\) mm |
| 3. | \(0.1\) mm | 4. | \(0.15\) mm |
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In the CGS system, Young's modulus of a steel wire is \(2\times 10^{12}~\text{dyne/cm}^2.\) To double the length of a wire of unit cross-section area, the force required is:
1. \(4\times 10^{6}~\text{dynes}\)
2. \(2\times 10^{12}~\text{dynes}\)
3. \(2\times 10^{12}~\text{newtons}\)
4. \(2\times 10^{8}~\text{dynes}\)
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Steel and copper wires of the same length and area are stretched by the same weight one after the other. Young's modulus of steel and copper are \(2\times10^{11} ~\text{N/m}^2\) and \(1.2\times10^{11}~\text{N/m}^2.\) The ratio of increase in length is:
| 1. | \(2 \over 5\) | 2. | \(3 \over 5\) |
| 3. | \(5 \over 4\) | 4. | \(5 \over 2\) |
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Two wires of copper having length in the ratio of \(4:1\) and radii ratio of \(1:4\) are stretched by the same force. The ratio of longitudinal strain in the two will be:
| 1. | \(1:16\) | 2. | \(16:1\) |
| 3. | \(1:64\) | 4. | \(64:1\) |
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| 1. | stress\(\times\)strain |
| 2. | \(\frac{1}{2}\)\(\times\)stress\(\times\)strain |
| 3. | \(2\times\)stress\(\times\)strain |
| 4. | stress/strain |
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A \(5~\text{m}\) long wire is fixed to the ceiling. A weight of \(10~\text{kg}\) is hung at the lower end and is \(1~\text{m}\) above the floor. The wire was elongated by \(1~\text{mm}.\) The energy stored in the wire due to stretching is:
1. zero
2. \(0.05~\text J\)
3. \(100~\text J\)
4. \(500~\text J\)
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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. \(\frac{E}{Y}\)
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