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: Â Stress - Strain |
Level 4: Below 35%
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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: Â Stress - Strain |
Level 3: 35%-60%
Hints
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: Â Stress - Strain |
Level 3: 35%-60%
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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: Â Stress - Strain |
Level 3: 35%-60%
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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: Â Stress - Strain |
Level 3: 35%-60%
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A uniform rod of mass \(m,\) having cross-section \(A\) is pushed along its length \((L)\) by means of a force of magnitude, \(F.\) There is no friction anywhere. Ignore the weight of the rod. The longitudinal stress in the rod, at a distance \(\dfrac{L}{3}\) from the left end, is:
| 1. | tensile, \(\dfrac{F}{3A}\) | 2. | compressive, \(\dfrac{F}{3A}\) |
| 3. | tensile, \(\dfrac{2F}{3A}\) | 4. | compressive, \(\dfrac{2F}{3A}\) |
Subtopic: Â Stress - Strain |
Level 3: 35%-60%
Hints
One end of uniform wire of length \(L\) and of weight \(W\) is attached rigidly to a point in a roof and a weight \(W_1\) is suspended from the lower end. If \(A\) is area of cross-section of the wire, the stress in the wire at a height \(3L \over 4\) from its lower end is:
1. \(W_1 \over A\)
2. \(\frac{\left(W_1+\frac{W}{4}\right)}{A} \)
3. \(\left(W_1+ {3W \over 4}\right) \over A\)
4. \(W_1 + W \over A\)
1. \(W_1 \over A\)
2. \(\frac{\left(W_1+\frac{W}{4}\right)}{A} \)
3. \(\left(W_1+ {3W \over 4}\right) \over A\)
4. \(W_1 + W \over A\)
Subtopic: Â Stress - Strain |
 76%
Level 2: 60%+
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Two identical blocks, which are connected by means of a light metallic wire of cross-sectional area \(\alpha,\) are dragged along a smooth horizontal plane by means of a horizontal force \(F.\) The stress in the wire is:
| 1. | zero | 2. | \(\dfrac{F}{\alpha}\) |
| 3. | \(\dfrac{F}{2\alpha}\) | 4. | \(\dfrac{2F}{\alpha}\) |
Subtopic: Â Stress - Strain |
Level 3: 35%-60%
Hints
An extremely long solid rod of length \(L\) starts falling longitudinally towards a large point mass \(M,\) the near end of the rod being at a distance \(L\) from the mass \(M.\)
The rod experiences:
The rod experiences:
| 1. | no stress | 2. | compressive stress |
| 3. | tensile stress | 4. | shear stress |
Subtopic: Â Stress - Strain |
Level 3: 35%-60%
Hints
A rod of length \(L\) is pulled along its length by means of a pulling force \(F,\) which causes it to accelerate. The cross-section of the rod is uniform and equals \(A.\) The average stress in the rod equals:
| 1. | \(\dfrac{F}{A}\) | 2. | \(\dfrac{F}{2A}\) |
| 3. | \(\dfrac{F}{3A}\) | 4. | \(\dfrac{F}{4A}\) |
Subtopic: Â Stress - Strain |
 52%
Level 3: 35%-60%
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