Q. No.1. infinity
2. zero
3. unity
4. some finite small non-zero constant value
The maximum load a wire can withstand without breaking when its length is reduced to half of its original length, will:
1. be doubled
2. be halved
3. be four times
4. remain the same
The temperature of the wire is doubled. Young's modulus of elasticity:
| 1. | will also double. | 2. | will become four times. |
| 3. | will remain the same. | 4. | will decrease. |
A spring is stretched by applying a load to its free end. The strain produced in the spring is:
1. volumetric2. shear
3. longitudinal and shear
4. longitudinal
A rigid bar of mass \(M\) is supported symmetrically by three wires each of length \(l\). Those at each end are of copper and the middle one is of iron. The ratio of their diameters, if each is to have the same tension, is equal to:
| 1. | \(\dfrac{Y_{\text{copper}}}{ Y_{\text{iron}}}\) | 2. | \({\sqrt{\dfrac{Y_{\text{iron}}}{Y_{\text{copper}}}}}\) |
| 3. | \({\dfrac{Y^{2}_{\text{iron}}}{Y^{2}_{\text{copper}}}}\) | 4. | \({\dfrac{Y_{\text{iron}}}{Y_{\text{copper}}}}\) |
A mild steel wire of length \(2L\) and cross-sectional area \(A\) is stretched, well within the elastic limit, horizontally between two pillars (figure). A mass \(m\) is suspended from the mid-point of the wire. Strain in the wire is:
| 1. | \( \dfrac{x^2}{2 L^2} \) | 2. | \(\dfrac{x}{\mathrm{~L}} \) |
| 3. | \(\dfrac{x^2}{L}\) | 4. | \(\dfrac{x^2}{2L}\) |
A rectangular frame is to be suspended symmetrically by two strings of equal length on two supports (figure). It can be done in one of the following three ways;
The tension in the strings will be:
| 1. | the same in all cases. | 2. | least in (a). |
| 3. | least in (b). | 4. | least in (c). |
| 1. | Both the rods will elongate but there shall be no perceptible change in shape. |
| 2. | The steel rod will elongate and change shape but the rubber rod will only elongate. |
| 3. | The steel rod will elongate without any perceptible change in shape but the rubber rod will elongate and the shape of the bottom edge will change to an ellipse. |
| 4. | The steel rod will elongate without any perceptible change in shape but the rubber rod will elongate with the shape of the bottom edge tapered to a tip at the centre. |
The stress-strain graphs for the two materials are shown in the figure. (assumed 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) |
The correct statements are:
1. (a), (c)
2. (c), (d)
3. (b), (c)
4. (b), (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 \(F.\) |
The correct statements are:
| 1. | (a), (b) | 2. | (a), (d) |
| 3. | (b), (c) | 4. | (a), (c) |
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