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Q. No.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
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 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). |
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
\((Y_{\text{Al}}=70\times10^9~\text{N/m}^2\) 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) |
1. \(\frac{x^2}{2 L^2} \)
2. \(\frac{x}{L}\)
3. \(\frac{x^2}{L} \)
4. \(\frac{x^2}{2 L}\)
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Q. No.
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