Q. No.A force \(F\) is needed to break a copper wire having radius \(R.\) The force needed to break a copper wire of radius \(2R\) will be:
| 1. | \(F/2\) | 2. | \(2F\) |
| 3. | \(4F\) | 4. | \(F/4\) |
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1. \(7.06\times 10^{4}~\text{N}\)
2. \(5.03\times 10^{4}~\text{N}\)
3. \(1.09\times 10^{4}~\text{N}\)
4. \(17\times 10^{4}~\text{N}\)
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The breaking stress of a wire going over a smooth pulley in the following question is \(2\times 10^{9}~\text{N/m}^2.\) What would be the minimum radius of the wire used if it is not to break?
| 1. | \(0.46\times10^{-6}~\text{m}\) | 2. | \(0.46\times10^{-4}~\text{m}\) |
| 3. | \(0.46\times10^{8}~\text{m}\) | 4. | \(0.46\times10^{-11}~\text{m}\) |
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A light rod of length \(2~\text{m}\) 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 \(A_1 = 0.1~\text{cm}^2\) and brass wire of cross-sectional area \(A_2 = 0.2~\text{cm}^2.\) To have equal stress in both wires, \(\frac{T_1}{T_2}?\)
| 1. | \(\dfrac{1}{3}\) | 2. | \(\dfrac{1}{4}\) |
| 3. | \(\dfrac{4}{3}\) | 4. | \(\dfrac{1}{2}\) |
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To break a wire, a force of \(10^6~\text{N/m}^{2}\) is required. If the density of the material is \(3\times 10^{3}~\text{kg/m}^3,\) then the length of the wire which will break by its own weight will be:
1. \(34~\text m\)
2. \(30~\text m\)
3. \(300~\text m\)
4. \(3~\text m\)
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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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lf \(\rho\) is the density of the material of a wire and \(\sigma\) is the breaking stress, the greatest length of the wire that can hang freely without breaking is:
1. \(\dfrac{2}{\rho g}\)
2. \(\dfrac{\rho}{\sigma g}\)
3. \(\dfrac{\rho g}{2 \sigma}\)
4. \(\dfrac{\sigma}{\rho g}\)
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The breaking stress of a wire depends on:
| 1. | length of the wire |
| 2. | applied force |
| 3. | material of the wire |
| 4. | area of the cross-section of the wire |
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One end of a uniform wire of length \(L\) and of weight \(W\) is attached rigidly to a point in the roof and a weight \(W_1\) is suspended from its lower end. If \(A\) is the area of the cross-section of the wire, the stress in the wire at a height \(\frac{3L}{4}\) from its lower end is:
1. \(\frac{W+W_1}{A}\)
2. \(\frac{4W+W_1}{3A}\)
3. \(\frac{3W+W_1}{4A}\)
4. \(\frac{\frac{3}{4}W+W_1}{A}\)
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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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