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. | \(0.46\times10^{-11}~\text{m}\) |
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 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. |
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 |
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 |
The edge of an aluminium cube is \(10\) cm long. One face of the cube is firmly fixed to a vertical wall. A mass of \(100\) kg is then attached to the opposite face of the cube. The shear modulus of aluminium is \(25\) GPa. What is the vertical deflection of this face?
1. | \(4.86\times 10^{-6}~\text{m}\) | 2. | \(3.92\times 10^{-7}~\text{m}\) |
3. | \(3.01\times 10^{-7}~\text{m}\) | 4. | \(6.36\times 10^{-7}~\text{m}\) |