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Q. No.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 \(\cos\theta?\)
1.
2.
3.
4.
Subtopic: Stress - Strain Curve |
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A solid metallic sphere is subjected to an external pressure of \(p.\) The bulk modulus of the material of the sphere is \(B.\) The change in the magnitude of the middle cross-sectional area of the sphere \((\Delta A)\) equals: (initial area = \(A\))
| 1. | \(\dfrac{pA}{B}\) | 2. | \(\dfrac{pA}{3B}\) |
| 3. | \(\dfrac{2pA}{3B}\) | 4. | \(\dfrac{pA}{2B}\) |
Subtopic: Shear and bulk modulus |
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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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Two rods having the same cross-section (area: \(A\)) are joined end-to-end and forces \(F,F\) are applied at the two ends, as shown.
The lengths of the rods (\(I\) & \(II\)) are \(L,2L\) while the Young's moduli are \(2Y,Y\) respectively. Quantities associated with this system are mentioned in Column-I, while their values are indicated in Column-II but in a different order. Match them.
The lengths of the rods (\(I\) & \(II\)) are \(L,2L\) while the Young's moduli are \(2Y,Y\) respectively. Quantities associated with this system are mentioned in Column-I, while their values are indicated in Column-II but in a different order. Match them.
| Column-I | Column-II | ||
| (A) | \(\dfrac{\text{stress in rod }I}{\text{stress in rod } II}\) | (I) | \(\dfrac14\) |
| (B) | \(\dfrac{\text{strain in rod }I}{\text{strain in rod } II}\) | (II) | \(\dfrac12\) |
| (C) | \(\dfrac{\text{change in length of rod }I}{\text{change in length of rod }II}\) | (III) | \(1\) |
| (D) | \(\dfrac{\text{elastic energy stored in rod }I}{\text{elastic energy stored in rod }II}\) | (IV) | \(2\) |
| 1. | A-II, B-IV, C-I, D-III |
| 2. | A-III, B-IV, C-I, D-II |
| 3. | A-IV, B-II, C-I, D-III |
| 4. | A-III, B-II, C-I, D-I |
Subtopic: Stress - Strain |
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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: Stress - Strain |
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Two plates \(A,B\) are bolted together by means of a bolt \(PQ\) so that they move together. External forces \(F_1,F_2\) act along the planes of the plates. The material of the bolt \(PQ\) should have:
| 1. | small Young's modulus |
| 2. | large Young's modulus |
| 3. | small shear modulus |
| 4. | large shear modulus |
Subtopic: Shear and bulk modulus |
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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: 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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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: Stress - Strain |
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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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