Q. No.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.
\(40~\text{N}\)
A uniform rod suspended from the ceiling gets elongated by its weight. Which one of the following graphs represents the variation of elongation with length, \(L\)?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Aluminium and iron rods of the same length and same diameter are combined together as shown in the figure. A force \(F\) is applied at one of the ends. The combined length is increased by \(2\) cm. The rods will have:
| 1. | same stress and strain. |
| 2. | different stress and strain. |
| 3. | same stress and different strain. |
| 4. | same strain and different stress. |
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. |  |
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 \(0.03\)%. |
A wire of length \(L,\) area of cross section \(A\) is hanging from a fixed support. The length of the wire changes to \({L}_1\) when mass \(M\) is suspended from its free end. The expression for Young's modulus is:
| 1. | \(\dfrac{{Mg(L}_1-{L)}}{{AL}}\) | 2. | \(\dfrac{{MgL}}{{AL}_1}\) |
| 3. | \(\dfrac{{MgL}}{{A(L}_1-{L})}\) | 4. | \(\dfrac{{MgL}_1}{{AL}}\) |
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 |
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