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Q. No.A uniform rod \(AB\) is rotated at a constant angular speed about its end \(A,\) the rotation axis being perpendicular to \(AB.\) During rotation, stresses are set up in the rod. Let the stress at \(A\) be \(\sigma_A\) and that at the centre \(C\) be \(\sigma_C.\) Then:
1. \(\sigma_A=\sigma_C\)
2. \(\sigma_A=2\sigma_C\)
3. \(\sigma_C=2\sigma_A\)
4. \(\sigma_C=\dfrac34\sigma_A\)
1. \(\sigma_A=\sigma_C\)
2. \(\sigma_A=2\sigma_C\)
3. \(\sigma_C=2\sigma_A\)
4. \(\sigma_C=\dfrac34\sigma_A\)
Subtopic: Stress - Strain |
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A simple pendulum \((OA)\) of length \(l\) is suspended from a point \(O,\) and the bob (mass : \(m\)) is given a transverse velocity, \(u=\sqrt{4gl}\) at its lowest point. When the suspended wire makes an angle \(\theta\) with the vertical, the stress in the wire is \(S.\)
Which, of the following, shows the proper dependence of \(S\) as a function of \(\cos\theta?\)
Which, of the following, shows the proper dependence of \(S\) as a function of \(\cos\theta?\)
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Stress - Strain Curve |
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A wire has a length \(l_1\) when it is under tension \(T_1,\) and length \(l_2\) when it is under tension \(T_2.\) When it is under a tension \(T_1 + T_2,\) its length is:
1. \(l_1+l_2\)
2. \(\dfrac{l_1T_1+l_2T_2}{T_1+T_2}\)
3. \(\dfrac{l_1T_1-l_2T_2}{T_1-T_2}\)
4. \(\dfrac{l_1T_2+l_2T_1}{T_1+T_2}\)
Subtopic: Young's modulus |
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A cube made of a homogeneous, isotropic elastic solid is acted upon by forces of equal magnitude acting perpendicular to its opposite faces as shown. Forces are applied uniformly over the area of each face. The stress at the centre of the cube is:
1. tensile
2. compressive
3. shear
4. zero
1. tensile2. compressive
3. shear
4. zero
Subtopic: Stress - Strain |
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A simple pendulum of length \(l\) is suspended from \(O,\) and is released from rest from a horizontal position. The cross-section of the connecting wire is \(A\) and, Young's modulus is \(Y.\) The mass of the bob is \(m.\) When the bob swings to the lowest position, the strain in the wire is:
| 1. | \(\dfrac{mg}{AY}\) | 2. | \(\dfrac{2mg}{AY}\) |
| 3. | \(\dfrac{3mg}{AY}\) | 4. | \(\dfrac{mg}{2AY}\) |
Subtopic: Stress - Strain |
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A large cylindrical piece of a dense solid elastic metal stands on its end as shown in the figure. The metal is uniform and isotropic. The stress in the material as a function of height is shown correctly by:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Stress - Strain Curve |
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Two wires of identical dimensions but of different materials having Young's moduli \(Y_1, Y_2\) are joined end to end. When the first wire is under a tension \(T,\) it elongates by \(x_1\) while the second wire elongates by \(x_2\) under the same tension \(T.\) The elongation of the composite wire when it is under tension \(T\) is:
| 1. | \(x_1+x_2\) | 2. | \(\dfrac{Y_1x_1+Y_2x_2}{Y_1+Y_2}\) |
| 3. | \(\dfrac{x_1+x_2}{2}\) | 4. | \(\dfrac{Y_1x_2+Y_2x_1}{Y_1+Y_2}\) |
Subtopic: Young's modulus |
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Two equal and opposite forces, each of magnitude \(F,\) are applied along a rod of transverse sectional area \(A.\) The normal stress on a section \(PQ\) inclined at an angle \(\theta\) to the transverse section is given by:
| 1. | \(\dfrac{F}{A} \mathrm{sin \theta}\) | 2. | \(\dfrac{F}{A} \mathrm{cos \theta}\) |
| 3. | \(\dfrac{F}{2A} \mathrm{sin2 \theta}\) | 4. | \(\dfrac{F}{A} \mathrm{cos^2 \theta}\) |
Subtopic: Stress - Strain |
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Consider a uniform beam \(\text{AB},\) which is being pulled by a horizontal force \(F\) applied at the end \(\text A,\) so that it is accelerated uniformly. The cross-section of the beam is \(A.\) Let the stress at the ends \(\text A,\text B\) be \(S_\text A,S_\text B\) and that at the centre \(\text C\) be \(S_\text C.\) Then:
| 1. | \(S_\text A=\text{zero},S_\text B=\text{maximum,}\) \(S_\text C=\text{intermediate}\) |
| 2. | \(S_\text A=\text{maximum, }S_\text B=0,\) \(S_\text C=\text{intermediate}\) |
| 3. | \(S_\text A=S_\text B=\text{maximum},\) \(S_\text C=\text{zero}\) |
| 4. | \(S_\text A=S_\text B=S_\text C=\text{constant throughout}\) |
Subtopic: Stress - Strain |
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A uniform rod of mass \(10~\text{kg}\) and length \(6~\text m\) is hanged from the ceiling as shown in the figure. Given the area of the cross-section of rod \(3~\text{mm}^2\) and Young’s modulus is \(2\times10^{11}~\text{N/m}^2.\) The extension in the rod’s length is:
(Take \(g=10~\text{m/s}^2\))
1. \(1~\text{mm}\)
2. \(0.5~\text{mm}\)
3. \(0.25~\text{mm}\)
4. \(1.2~\text{mm}\)
(Take \(g=10~\text{m/s}^2\))
1. \(1~\text{mm}\)
2. \(0.5~\text{mm}\)
3. \(0.25~\text{mm}\)
4. \(1.2~\text{mm}\)
Subtopic: Elasticity |
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