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. \(19.6\times 10^{-8}~\text{N/m}^2\)
If \(\mathrm{E}\) is the energy stored per unit volume in a wire having \(\mathrm{Y}\) as Young's modulus of the material, then the stress applied is:
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2.
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4.
A uniform cube is subjected to volume compression. If each side is decreased by \(1\%\), then bulk strain is:
| 1. | \(0.01\) | 2. | \(0.06\) |
| 3. | \(0.02\) | 4. | \(0.03\) |
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. | \(4a-3b\) |
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 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 elongation (\(X\)) of a steel wire varies with the elongating force (\(F\)) according to the graph: (within elastic limit)
| 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 |
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. | \(40~\text{N}\) |
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