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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 \(L \over 3\) from the left end, is:
1.
tensile, \(F \over 3A\)
2.
compressive, \(F \over 3A\)
3.
tensile, \(2F \over 3A\)
4.
compressive, \(2F \over 3A\)
Subtopic: Stress - Strain |
From NCERT
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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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The breaking stress in two wires of different materials \(A,B\) are in the ratio: \(\frac{S_A}{S_B}=\frac12,\) while their radii are in the ratio: \(\frac{r_A}{r_B}=\frac12.\) The tensions under which they break are \(T_A\) and \(T_B.\) Then \(\frac{T_A}{T_B}=\)?
1. \(2\)
2. \(\frac14\)
3. \(\frac18\)
4. \(\frac1{2\sqrt2}\)
1. \(2\)
2. \(\frac14\)
3. \(\frac18\)
4. \(\frac1{2\sqrt2}\)
Subtopic: Stress - Strain |
74%
From NCERT
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The elastic energy density in a stretched wire is:
1. (stress)2 × strain
2. stress × strain
3. \(\frac12\) × stress × strain
4. stress × (strain)2
1. (stress)2 × strain
2. stress × strain
3. \(\frac12\) × stress × strain
4. stress × (strain)2
Subtopic: Potential energy of wire |
91%
From NCERT
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Given below are two statements:
| Assertion (A): | The stretching of a spring is determined by the shear modulus of the material of the spring. |
| Reason (R): | A coil spring of copper has more tensile strength than a steel spring of the same dimensions. |
| 1. | Both (A) and (R) are true and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are true but (R) is not the correct explanation of (A). |
| 3. | (A) is false but (R) is true. |
| 4. | (A) is true but (R) is false. |
Subtopic: Shear and bulk modulus |
From NCERT
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If two identically shaped rods are joined end to end and compressive forces are applied to the system, the compressive strain will be:
| 1. | larger in the rod with a larger Young's modulus |
| 2. | larger in the rod with a smaller Young's modulus |
| 3. | equal in both the rods |
| 4. | negative in the rod with a smaller Young's modulus |
Subtopic: Young's modulus |
65%
From NCERT
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A wire of cross-section \(A_{1}\) and length \(l_1\) breaks when it is under tension \(T_{1};\) a second wire made of the same material but of cross-section \(A_{2}\) and length \(l_2\) breaks under tension \(T_{2}.\) A third wire of the same material having cross-section \(A,\) length \(l\) breaks under tension \(\frac{T_1+T_2}{2}\). Then,
| 1. | \(A=\frac{A_1+A_2}{2},~l=\frac{l_1+l_2}{2}\) |
| 2. | \(l=\frac{l_1+l_2}{2}\) |
| 3. | \(A=\frac{A_1+A_2}{2}\) |
| 4. | \(A=\frac{A_1T_1+A_2T_2}{2(T_1+T_2)},~l=\frac{l_1T_1+l_2T_2}{2(T_1+T_2)}\) |
Subtopic: Young's modulus |
From NCERT
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When a metal wire elongates by hanging a load on it, the gravitational potential energy is decreased.
| 1. | this energy completely appears as the increased kinetic energy of the block |
| 2. | this energy completely appears as the increased elastic potential energy of the wire |
| 3. | this energy completely appears as heat |
| 4. | none of these |
Subtopic: Potential energy of wire |
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A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break:
| 1. | when the mass is at the highest point |
| 2. | when the mass is at the lowest point |
| 3. | when the wire is horizontal |
| 4. | at an angle of \(\cos^{-1}(\frac{1}{3})\) from the upward vertical |
Subtopic: Stress - Strain |
73%
From NCERT
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The length of a metal wire is \(l_1\) when the tension in it is \(T_1\) and is \(l_2\) when the tension is \(T_2.\) The natural length of the wire is:
1. \(\frac{l_{1}+l_{2}}{2}\)
2. \(\sqrt{l_{1} l_{2}}\)
3. \(\frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}}\)
4. \(\frac{l_{1} T_{2}+l_{2} T_{1}}{T_{2}+T_{1}}\)
Subtopic: Young's modulus |
67%
From NCERT
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