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.
\(0.46\times10^{-11}~\text{m}\)
The Poisson's ratio of a material is \(0.4.\) If a force is applied to a wire of this material, there is a decrease in the cross-section area by \(2\)%. In such a case the percentage increase in its length will be:
| 1. | \(3\)% | 2. | \(2.5\)% |
| 3. | \(1\)% | 4. | \(0.5\)% |
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. | \(40~\text{N}\) |
Two wires \(X\) and \(Y\) of the same length are made of the same material. The figure represents the load \(F\) versus extension \(\Delta x\) graph for the two wires. Hence:
| 1. | Modulus of elasticity of \(Y\) is greater than that of \(X\). |
| 2. | Stiffness of \(Y\) is more than that of \(X\). |
| 3. | The cross-sectional area of \(Y\) is less than that of \(X\). |
| 4. | All of these |
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. |  |
| 1. | \(0\) | 2. | \(0.50\) |
| 3. | \(-0.5\) | 4. | Infinity |
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 \(0.03\)%. |
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