Q. No.A ball falling into a lake of depth \(200~\text{m}\) shows a \(0.1\%\) decrease in its volume at the bottom. What is the bulk modulus of the material of the ball?
1. \(19.6\times 10^{8}~\text{N/m}^2\)
2. \(19.6\times 10^{-10}~\text{N/m}^2\)
3. \(19.6\times 10^{10}~\text{N/m}^2\)
4. \(19.6\times 10^{-8}~\text{N/m}^2\)
1. \(19.6\times 10^{8}~\text{N/m}^2\)
2. \(19.6\times 10^{-10}~\text{N/m}^2\)
3. \(19.6\times 10^{10}~\text{N/m}^2\)
4. \(19.6\times 10^{-8}~\text{N/m}^2\)
The length of an elastic string is \(a\) metre when the longitudinal tension is \(4\) N and \(b\) metre when the longitudinal tension is \(5\) N. The length of the string in metre when the longitudinal tension is \(9\) N will be:
| 1. | \(a-b\) | 2. | \(5b-4a\) |
| 3. | \(2b-\frac{1}{4}a\) | 4. | \(4a-3b\) |
1. \(40 \times 10^8~\text{Nm}^{-2}\)
2. \(20 \times 10^8~\text{Nm}^{-2}\)
3. \(10 \times 10^8~\text{Nm}^{-2}\)
4. \(5 \times 10^8~\text{Nm}^{-2}\)
Two wires of copper having the length in the ratio \(4:1\) and their radii ratio as \(1:4\) are stretched by the same force. The ratio of longitudinal strain in the two wires will be:
| 1. | \(1:16\) | 2. | \(16:1\) |
| 3. | \(1:64\) | 4. | \(64:1\) |
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 \(0.03\)%. |
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 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 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. |
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. |
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. |  |
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