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 |
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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. $$\frac1{2\sqrt2}$$
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
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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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 |
66%
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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 |
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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%
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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 |
66%
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