The stress-strain curves are drawn for two different materials \(X\) and \(Y.\) It is observed that the ultimate strength point and the fracture point are close to each other for material \(X\) but are far apart for material \(Y.\) We can say that the materials \(X\) and \(Y\) are likely to be (respectively):
1. | ductile and brittle |
2. | brittle and ductile |
3. | brittle and plastic |
4. | plastic and ductile |
1. | \(1 \times 10^6~\text{N/m}^2\) | 2. | \(2 \times 10^7~\text{N/m}^2\) |
3. | \(4 \times 10^8~\text{N/m}^2\) | 4. | \(6 \times 10^{10}~\text{N/m}^2\) |
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. | \(4a-3b\) |
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. | \(0.03\) |
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. \(19.6\times 10^{-8}~\text{N/m}^2\)
If \(E\) is the energy stored per unit volume in a wire having \(Y\) as Young's modulus of the material, then the stress applied is:
1. \(\sqrt{2EY}\)
2. \(2\sqrt{EY}\)
3. \(\frac{1}{2}\sqrt{EY}\)
4. \(\frac{3}{2}\sqrt{EY}\)
A light rod of length \(2~\text{m}\) is suspended from the ceiling horizontally by means of two vertical wires of equal length. A weight \(W\) is hung from the light rod as shown in the figure. The rod is hung by means of a steel wire of cross-sectional area \(A_1 = 0.1~\text{cm}^2\) and brass wire of cross-sectional area\(A_2 = 0.2~\text{cm}^2\). To have equal stress in both wires, \(\frac{T_1}{T_2}?\)
1. | \(1/3\) | 2. | \(1/4\) |
3. | \(4/3\) | 4. | \(1/2\) |
1. | \({AE} \frac{R}{r} \) | 2. | \(A E \left(\frac{R-r}{r}\right)\) |
3. | \(\frac{E}{A}\left(\frac{R-r}{A}\right)\) | 4. | \(\frac{Er}{AR}\) |
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. | \(0.02\)%. | decrease by2. | \(0.01\)%. | decrease by
3. | \(0.04\)%. | decrease by4. | \(0.03\)%. | increase by
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 |