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Q. No.Wire \({A}\) and \({B}\) have their Young's modulii in the ratio \(1:3\) area of the cross-section in the ratio of \(1:2\) and lengths in the ratio of \(3:4.\) If the same force is applied on the two wires to elongate then the ratio of elongation is equal to:
1. \(8:1\)
2. \(1:12\)
3. \(1:8\)
4. \(9:2\)
Subtopic: Young's modulus |
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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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Two blocks, one with a mass of \(2~\text{kg}\) and the other with a mass of \(1.14~\text{kg},\) are suspended by steel and brass wires, respectively, as shown in the figure. Given Young's moduli for steel and brass as \(2\times10^{11}~\text{N}/\text{m}^2\) and \(1\times10^{11}~\text{N}/\text{m}^2\) respectively, what is the change in the length for the steel wire?
| 1. | \(3.2 ~\mu \text{m}\) | 2. | \(1.6 ~\mu \text{m}\) |
| 3. | \(0.8 ~\mu \text{m}\) | 4. | \(4.8 ~\mu \text{m}\) |
Subtopic: Elasticity |
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Choose the correct expression that relates Poisson’s ratio \(\sigma,\) bulk modulus \(B,\) and modulus of rigidity \(G.\)
1. \(\mathit{\sigma}{=}\dfrac{{3}{B}{-}{2}{G}}{{2}{G}{+}{6}{B}}\)
2. \(\mathit{\sigma}{=}\dfrac{{6}{B}{+}{2}{G}}{{3}{B}{-}{2}{G}}\)
3. \(\mathit{\sigma}{=}\dfrac{9BG}{{3}{B}{+}{G}}\)
4. \({B}{=}\dfrac{{3}\mathit{\sigma}{-}{3}{G}}{{6}\mathit{\sigma}{+}{2}{G}}\)
1. \(\mathit{\sigma}{=}\dfrac{{3}{B}{-}{2}{G}}{{2}{G}{+}{6}{B}}\)
2. \(\mathit{\sigma}{=}\dfrac{{6}{B}{+}{2}{G}}{{3}{B}{-}{2}{G}}\)
3. \(\mathit{\sigma}{=}\dfrac{9BG}{{3}{B}{+}{G}}\)
4. \({B}{=}\dfrac{{3}\mathit{\sigma}{-}{3}{G}}{{6}\mathit{\sigma}{+}{2}{G}}\)
Subtopic: Elasticity |
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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 uniform rod of mass \(10~\text{kg}\) and length \(6~\text m\) is suspended vertically from the ceiling, as shown in the figure. The cross-sectional area of the rod is \(3~\text{mm}^2,\) and its Young’s modulus is \(2\times10^{11}~\text{N/m}^2.\) The extension in the length of the rod is: (take \(g=10~\text{m/s}^2\))
1. \(1~\text{mm}\)
2. \(0.5~\text{mm}\)
3. \(0.25~\text{mm}\)
4. \(1.2~\text{mm}\)
1. \(1~\text{mm}\)
2. \(0.5~\text{mm}\)
3. \(0.25~\text{mm}\)
4. \(1.2~\text{mm}\)
Subtopic: Elasticity |
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The elongation of a wire on the surface of the Earth is \(10^{-4}\) m. The same wire, of the same dimensions, elongates by \( 6 \times 10^{-5} \) m on another planet. The acceleration due to gravity on the planet will be:
(take acceleration due to gravity on the surface of the Earth as \(10\) m s-2)
1. \(5\) ms-2
2. \(6\) ms-2
3. \(7\) ms-2
4. \(8\) ms-2
(take acceleration due to gravity on the surface of the Earth as \(10\) m s-2)
1. \(5\) ms-2
2. \(6\) ms-2
3. \(7\) ms-2
4. \(8\) ms-2
Subtopic: Young's modulus |
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The elastic behaviour of a material for linear stress and linear strain is captured in the graph below. The energy density, for a linear strain of \(5 \times 10^{-4} \) is:
\((\)assume that the material is elastic up to the linear strain of \(5 \times 10^{-4})\)
\((\)assume that the material is elastic up to the linear strain of \(5 \times 10^{-4})\)
| 1. | \(15\) kJ/m3 | 2. | \(20\) kJ/m3 |
| 3. | \(25\) kJ/m3 | 4. | \(30\) kJ/m3 |
Subtopic: Stress - Strain Curve |
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The bulk modulus of a liquid is \(3\times10^{10}\) Nm–2. The pressure required to reduce the volume of liquid by \(2\text{%}\) is:
1. \(3\times10^{8}\) Nm–2
2. \(9\times10^{8}\) Nm–2
3. \(6\times10^{8}\) Nm–2
4. \(12\times10^{8}\) Nm–2
1. \(3\times10^{8}\) Nm–2
2. \(9\times10^{8}\) Nm–2
3. \(6\times10^{8}\) Nm–2
4. \(12\times10^{8}\) Nm–2
Subtopic: Shear and bulk modulus |
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A metal wire of length \(0.5\) m and cross-sectional area \(10^{-4}\) m2 has breaking stress \(5\times10^{8}\) Nm–2. A block of \(10\) kg is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of the block will be:
1. \(15\) m/s
2. \(50\) m/s
3. \(25\) m/s
4. \(40\) m/s
1. \(15\) m/s
2. \(50\) m/s
3. \(25\) m/s
4. \(40\) m/s
Subtopic: Stress - Strain |
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