Q. No.
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, \(\dfrac{2F}{3A}\)
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| 1. | \(\dfrac{3 M g l}{A Y}\) | 2. | \(\dfrac{2 M g l}{A Y}\) |
| 3. | \(\dfrac{3 M g l}{2 A Y}\) | 4. | \(\dfrac{M g l}{A Y}\) |
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1. tensile2. compressive
3. shear
4. zero
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| 1. | no stress. | 2. | compressive stress. |
| 3. | tensile stress. | 4. | shear stress. |
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| 1. |  |
2. |  |
| 3. |  |
4. |  |
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| 1. | \(1\) | 2. | \(2\) |
| 3. | \(\sqrt 2\) | 4. | \(\dfrac12\) |
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1. \(\sigma_A=\sigma_C\)
2. \(\sigma_A=2\sigma_C\)
3. \(\sigma_C=2\sigma_A\)
4. \(\sigma_C=\dfrac34\sigma_A\)
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| 1. | \(B_1\) | 2. | \(2B_1\) |
| 3. | \( \dfrac {B_1}{2}\) | 4. | \(\dfrac {B_1}{\sqrt 2}\) |
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| 1. | \(2\) | 2. | \(\dfrac14\) |
| 3. | \(\dfrac18\) | 4. | \(\dfrac1{2\sqrt2}\) |
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| 1. | \(\text{(stress)}^2 × \text{strain}\) | 2. | \(\text{stress} × \text{strain}\) |
| 3. | \(\dfrac12\times \text{stress} × \text{strain}\) | 4. | \(\text{stress} × \text{(strain)}^2\) |
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