Q. No.A copper and a steel wire of the same diameter are connected end to end. A deforming force \(F\) is applied to this composite wire which causes a total elongation of \(1\) cm. The two wires will have:
(a)
the same stress
(b)
different stress
(c)
the same strain
(d)
different strain
Choose the correct option:
1.
(a), (b)
2.
(a), (d)
3.
(b), (c)
4.
(c), (d)
\((Y_{\text{Al}}=70\times10^9~\text{N/m}^2\) and \(Y_{\text{steel}}=200\times10^9~\text{N/m}^2)\)
| (a) | The mass \(m\) should be suspended close to wire \(A\) to have equal stresses in both wires. |
| (b) | The mass \(m\) should be suspended close to \(B\) to have equal stresses in both wires. |
| (c) | The mass \(m\) should be suspended in the middle of the wires to have equal stresses in both wires. |
| (d) | The mass \(m\) should be suspended close to wire \(A\) to have equal strain in both wires. |
The correct statements are:
| 1. | (b), (c) | 3. | (b), (d) |
| 2. | (a), (d) | 4. | (c), (d) |
A wire is suspended from the ceiling and stretched under the action of a weight \(F\) suspended from its other end. The force exerted by the ceiling on it is equal and opposite to the weight.
| (a) | Tensile stress at any cross-section \(A\) of the wire is \(F/A.\) |
| (b) | Tensile stress at any cross-section is zero. |
| (c) | Tensile stress at any cross-section \(A\) of the wire is \(2F/A.\) |
| (d) | Tension at any cross-section \(A\) of the wire is \(F.\) |
Choose the correct option from the given ones:
1. (a) and (b) only
2. (a) and (d) only
3. (b) and (c) only
4. (a) and (c) only
The stress-strain graphs for the two materials are shown in the figure.
(assumed the same scale)
| (a) | Material (ii) is more elastic than material (i) and hence material (ii) is more brittle |
| (b) | Material (i) and (ii) have the same elasticity and the same brittleness |
| (c) | Material (ii) is elastic over a larger region of strain as compared to (i) |
| (d) | Material (ii) is more brittle than material (i) |
Choose the correct statements from the given ones:
1. (a) and (c) only
2. (c) and (d) only
3. (b) and (c) only
4. (b) and (d) only
The stress-strain graphs for two materials are: (assume same scale).
1. Material (ii) is more elastic than material (i) and hence, material (ii) is more brittle.
2. Material (i) and (ii) have the same elasticity and the same brittleness.
3. Material (i) is elastic over a larger region of strain as compared to (ii).
4. Material (ii) is more brittle than material (i).
The figure given below shows the longitudinal stress vs longitudinal strain graph for a given material. Based on the given graph, Young's modulus of the material with the increase in strain will:
1. be variable.
2. first increase & then decrease.
3. first decrease & then increase.
4. remain constant.
The figure shows the stress-strain curve for a given material. Young's modulus for the material is:
The ratio of Young's modulus of wire \(A\) to wire \(B\) is:
1. \(3:1\)
2. \(1:3\)
3. \(\sqrt{3}:1\)
4. \(1: \sqrt{3}\)
A student plots a graph from his readings on the determination of Young modulus of a metal wire but forgets to put the labels (figure). The quantities on X and Y-axes may be respectively,
| (a) | weight hung and length increased |
| (b) | stress applied and length increased |
| (c) | stress applied and strain developed |
| (d) | length increased and the weight hung |
Choose the correct option:
| 1. | (a) and (b) |
| 2. | (b) and (c) |
| 3. | (a), (b) and (d) |
| 4. | all of these |
The diagram shows stress v/s strain curve for materials \(A\) and \(B\). From the curves, we infer that:
| 1. | \(A\) is brittle but \(B\) is ductile. |
| 2. | \(A\) is ductile and \(B\) is brittle. |
| 3. | Both \(A\) and \(B\) are ductile. |
| 4. | Both \(A\) and \(B\) are brittle. |
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