Q. No.The breaking stress of a wire going over a smooth pulley in the following question is \(2\times 10^{9}~\text{N/m}^2.\) 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 \(A\). |
Within the elastic limit, the elongation \(X\) of a steel wire varies with the applied force \(F\) as shown in the graph. Which of the following graphs correctly represents this relationship?
| 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. | decrease by \(0.02\)%. | 2. | decrease by \(0.01\)%. |
| 3. | decrease by \(0.04\)%. | 4. | increase by \(0.03\)%. |
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 aluminum cube is \(10~\text{cm}\) long. One face of the cube is firmly fixed to a vertical wall. A mass of \(100~\text{kg}\) is then attached to the opposite face of the cube. The shear modulus of aluminum is \(25~\text{GPa}.\) 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. \(6.36\times 10^{-7}~\text{m}\)
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