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Q. No.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 \(\cos^{-1}\left(\dfrac{1}{3}\right)\) from the upward vertical
Subtopic: Stress - Strain |
75%
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When a metal wire elongates by hanging a load on it, the gravitational potential energy decreases.
| 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 the above. |
Subtopic: Potential energy of wire |
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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 \(\dfrac{T_1+T_2}{2}.\) Then:
| 1. | \(A=\dfrac{A_1+A_2}{2},~l=\dfrac{l_1+l_2}{2}\) |
| 2. | \(l=\dfrac{l_1+l_2}{2}\) |
| 3. | \(A=\dfrac{A_1+A_2}{2}\) |
| 4. | \(A=\dfrac{A_1T_1+A_2T_2}{2(T_1+T_2)},~l=\dfrac{l_1T_1+l_2T_2}{2(T_1+T_2)}\) |
Subtopic: Young's modulus |
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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. | \(\dfrac{l_{1}+l_{2}}{2}\) | 2. | \(\sqrt{l_{1} l_{2}}\) |
| 3. | \(\dfrac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}}\) | 4. | \(\dfrac{l_{1} T_{2}+l_{2} T_{1}}{T_{2}+T_{1}}\) |
Subtopic: Young's modulus |
69%
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A rope \(1\) cm in diameter breaks if the tension in it exceeds \(500\) N. The maximum tension that may be given to a similar rope of diameter \(2\) cm is:
1. \(500\) N
2. \(250\) N
3. \(1000\) N
4. \(2000\) N
Subtopic: Young's modulus |
68%
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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: 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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The breaking stress in two wires of different materials \(A,B\) are in the ratio: \(\dfrac{S_A}{S_B}=\dfrac12,\) while their radii are in the ratio: \(\dfrac{r_A}{r_B}=\dfrac12.\) The tensions under which they break are \(T_A\) and \(T_B.\) Then \(\dfrac{T_A}{T_B}=\)?
| 1. | \(2\) | 2. | \(\dfrac14\) |
| 3. | \(\dfrac18\) | 4. | \(\dfrac1{2\sqrt2}\) |
Subtopic: Stress - Strain |
72%
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The elastic energy density in a stretched wire is:
| 1. | \(\text{(stress)}^2 × \text{strain}\) | 2. | \(\text{stress} × \text{strain}\) |
| 3. | \(\dfrac12\times \text{stress} × \text{strain}\) | 4. | \(\text{stress} × \text{(strain)}^2\) |
Subtopic: Potential energy of wire |
91%
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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 |
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