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. | volumetric |
2. | shear |
3. | longitudinal and shear |
4. | longitudinal |
A mild steel wire of length \(\mathrm{2L}\) 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 \(F.\) |
The correct statements are:
1. (a), (b)
2. (a), (d)
3. (b), (c)
4. (a), (c)
A rod of length \(l\) and negligible mass is suspended at its two ends by two wires of steel (wire \(A\)) and aluminium (wire \(B\)) of equal lengths (figure). The crosse-sectional areas of wires \(A\) and \(B\) are \(1.0~\text{mm}^2\) and \(2.0~\text{mm}^2\) respectively. \((Y_{\text{Al}}=70\times10^9~\text{N/m}^2\) and \(Y_{\text{steel}}=200\times10^9~\text{N/m}^2)\)
(a) | Mass \(m\) should be suspended close to wire \(A\) to have equal stresses in both wires. |
(b) | Mass \(m\) should be suspended close to \(B\) to have equal stresses in both wires. |
(c) | Mass \(m\) should be suspended in the middle of the wires to have equal stresses in both wires. |
(d) | Mass \(m\) should be suspended close to wire \(A\) to have equal strain in both wires. |
The correct statements are:
1. (b, c)
2. (a, d)
3. (b, d)
4. (c, d)