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Q. No.A steel wire having a radius of \(2.0\text{ mm},\) carrying a load of \(4\text{ kg},\) is hanging from a ceiling. Given that \(g=3.1\pi~\text{m/s}^{2} ,\) what will be the tensile stress that would be developed in the wire?
| 1. | \(5.2\times10^{6}~\text{N/m}^{2}\) | 2. | \(6.2\times10^{6}~\text{N/m}^{2}\) |
| 3. | \(4.8\times10^{6}~\text{N/m}^{2}\) | 4. | \(3.1\times10^{6}~\text{N/m}^{2}\) |
Subtopic: Stress - Strain |
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A block of mass \(M\) is attached to a prop on a smooth horizontal surface of a truck by means of a wire of length \(L,\) cross-section \(\alpha.\) Young's modulus of elasticity of the material of the wire is \(Y.\) The truck accelerates forward with an acceleration \(a=\dfrac{g}{2}.\) The change in length of the wire is:
| 1. | \({\dfrac{MgL}{\alpha Y}}\) | 2. | \({ \dfrac{MgL}{2\alpha Y}}\) |
| 3. | \({\dfrac{2MgL}{\alpha Y}}\) | 4. | \({ \dfrac{MgL}{4\alpha Y}}\) |
Subtopic: Stress - Strain |
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Level 1: 80%+
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Three blocks of masses \(1~\text{kg},2~\text{kg},2~\text{kg}\) lie in a line on a smooth horizontal plane, connected by two horizontal metallic wires (of negligible mass) – \(I\) & \(II.\) A horizontal force of \(10~\text{ N}\) acts on the \(1~\text{kg}\) block, as shown.
The cross-sectional area \((A),\) length \((L)\) and Young's moduli \((Y)\) of the wires are related by: \(A_I=2A_{II}\\ L_I=2L_{II}\\ Y_I=2Y_{II}\)
The ratio of the stresses in the wires (wire \(\mathrm I\)/\(\mathrm{II}\)) is:
1. \(1\)
2. \(2\)
3. \(\dfrac12\)
4. \(4\)
The cross-sectional area \((A),\) length \((L)\) and Young's moduli \((Y)\) of the wires are related by: \(A_I=2A_{II}\\ L_I=2L_{II}\\ Y_I=2Y_{II}\)
The ratio of the stresses in the wires (wire \(\mathrm I\)/\(\mathrm{II}\)) is:
1. \(1\)
2. \(2\)
3. \(\dfrac12\)
4. \(4\)
Subtopic: Stress - Strain |
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Level 1: 80%+
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A uniform metallic wire is elongated by \(0.04\) m when subjected to a linear force \(F\). The elongation, if its length and diameter are doubled and subjected to the same force will be:
| 1. | \(1\) cm | 2. | \(2 \) cm |
| 3. | \(3\) cm | 4. | \(6\) cm |
Subtopic: Stress - Strain |
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Level 1: 80%+
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A wire of length \(l,\) cross-sectional area \(A\) is pulled as shown. \(Y\) is Young’s modulus of wire. The elongation in wire is:
(\(F=100\) N, \(A=10\) cm2, \(l=1\) m, \(Y=5\times10^{10}\) N/m2)
1. \(10^{-6}\) m
2. \(10^{-5}\) m
3. \(2\times10^{-6}\) m
4. \(2\times10^{-5}\) m
(\(F=100\) N, \(A=10\) cm2, \(l=1\) m, \(Y=5\times10^{10}\) N/m2)
1. \(10^{-6}\) m
2. \(10^{-5}\) m
3. \(2\times10^{-6}\) m
4. \(2\times10^{-5}\) m
Subtopic: Stress - Strain |
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A rod is fixed at one end and other end is pulled with force \(F = 62.8\text{ kN},\) Young’s modulus of rod is \(2 × 10^{11} \text{ N/m}^2.\) If the radius of cross-section of rod is \(20\text{ mm}\) the strain produced in rod is:
1. \(2.5\times10^{-3}\)
2. \(2.5\times10^{-4}\)
3. \(2.0\times10^{-3}\)
4. \(2.0\times10^{-4}\)
1. \(2.5\times10^{-3}\)
2. \(2.5\times10^{-4}\)
3. \(2.0\times10^{-3}\)
4. \(2.0\times10^{-4}\)
Subtopic: Stress - Strain |
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The breaking stress of a wire depends on:
| 1. | material of the wire |
| 2. | length of the wire |
| 3. | radius of the wire |
| 4. | shape of the cross-section |
Subtopic: Stress - Strain |
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Consider two wires \(A\) and \(B\) which are made of same material. The diameter of \(A\) is four times larger than \(B.\) If they are stretched by same load, then the stress on \(B\) is:
1. equal to that on \(A\)
2. sixteen times that on \(A\)
3. twice that on \(A\)
4. half that on \(A\)
1. equal to that on \(A\)
2. sixteen times that on \(A\)
3. twice that on \(A\)
4. half that on \(A\)
Subtopic: Stress - Strain |
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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
Subtopic: Stress - Strain |
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A wire of length \(l,\) area of cross-section \(A,\) and Young's modulus of elasticity \(Y\) is stretched by a longitudinal force \(F.\) The change in length is \(\Delta l.\) Match the following two columns.
| Column-I | Column-II | ||
| \(\mathrm{(a)}\) | \(F\) is increased | \(\mathrm{(p)}\) | \(\Delta l\) will increase |
| \(\mathrm{(b)}\) | \(l\) is increased | \(\mathrm{(q)}\) | stress will increase |
| \(\mathrm{(c)}\) | \(A\) is increased | \(\mathrm{(r)}\) | \(\Delta l\) will decrease |
| \(\mathrm{(d)}\) | \(Y\) is increased | \(\mathrm{(s)}\) | stress will decrease |
| 1. | \(\mathrm{(a)-r, (b)-p,q, (c)-r, (d)-s}\) |
| 2. | \(\mathrm{(a)-p,q, (b)-p, (c)-r,s (d)-r}\) |
| 3. | \(\mathrm{(a)-p, (b)-r, (c)-s, (d)-p}\) |
| 4. | \(\mathrm{(a)-r, (b)-s, (c)-p,q, (d)-p}\) |
Subtopic: Stress - Strain |
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