The Young's modulus of a wire is numerically equal to the stress at a point when:
1. | The strain produced in the wire is equal to unity. |
2. | The length of the wire gets doubled. |
3. | The length increases by \(100\%.\) |
4. | All of these. |
A metallic rope of diameter \(1~ \text{mm}\) breaks at \(10 ~\text{N}\) force. If the wire of the same material has a diameter of \(2~\text{mm}\), then the breaking force is:
1. | \(2.5~\text{N}\) | 2. | \(5~\text{N}\) |
3. | \(20~\text{N}\) | 4. | \(40~\text{N}\) |
The breaking stress of a wire going over a smooth pulley in the following question is \(2\times 10^{9}\) N/. What would be the minimum radius of the wire used if it is not to break?
1. | \(0.46\times10^{-6}~\text{m}\) | 2. | \(0.46\times10^{-4}~\text{m}\) |
3. | \(0.46\times10^{8}~\text{m}\) | 4. | \(0.46\times10^{-11}~\text{m}\) |
The stress-strain curve for two materials \(A\) and \(B\) are as shown in the figure. Select the correct statement:
1. | Material \(A\) is less brittle and less elastic as compared to \(B\). |
2. | Material \(A\) is more ductile and less elastic as compared to \(B\). |
3. | Material \(A\) is less brittle and more elastic than \(B\). |
4. | Material \(B\) is more brittle and more elastic than \(A\). |
The elongation (\(X\)) of a steel wire varies with the elongating force (\(F\)) according to the graph: (within elastic limit)
1. | 2. | ||
3. | 4. |
A uniform wire of length \(3\) m and mass \(10\) kg is suspended vertically from one end and loaded at another end by a block of mass \(10\) kg. The radius of the cross-section of the wire is \(0.1\) m. The stress in the middle of the wire is: (Take \(g=10\) ms-2)
1. | \(1.4 \times10^4\) N/m2 | 2. | \(4.8 \times10^3\) N/m2 |
3. | \(96 \times10^4\) N/m2 | 4. | \(3.5\times10^3\) N/m2 |
The increase in the length of a wire on stretching is \(0.04\)%. If Poisson's ratio for the material of wire is \(0.5,\) then the diameter of the wire will:
1. | \(0.02\)%. | decrease by2. | \(0.01\)%. | decrease by
3. | \(0.04\)%. | decrease by4. | \(0.03\)%. | increase by
The stress versus strain graph is shown for two wires. If \(Y_1\) and \(Y_2\) are Young modulus of wire A and B respectively, then the correct option is:
1. | \(Y_1>Y_2\) | 2. | \(Y_2>Y_1\) |
3. | \(Y_1=Y_2\) | 4. | cannot say |
If \(E\) is the energy stored per unit volume in a wire having \(Y\) as Young's modulus of the material, then the stress applied is:
1. \(\sqrt{2EY}\)
2. \(2\sqrt{EY}\)
3. \(\frac{1}{2}\sqrt{EY}\)
4. \(\frac{3}{2}\sqrt{EY}\)
The stress-strain graphs for materials \(A\) and \(B\) are shown in the figure. Young’s modulus of material \(A\) is: (the graphs are drawn to the same scale):
1. | equal to material \(B\) |
2. | less than material \(B\) |
3. | greater than material \(B\) |
4. | can't say |