Q. No.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.
\(\dfrac{1}{3}\)
2.
\(\dfrac{1}{4}\)
3.
\(\dfrac{4}{3}\)
4.
\(\dfrac{1}{2}\)
| 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 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 |
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. \(64:1\)
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. \(5 \times 10^8~\text{Nm}^{-2}\)
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 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. \(19.6\times 10^{-8}~\text{N/m}^2\)
A wire can sustain a weight of 10 kg before breaking. If the wire is cut into two equal parts, then each part can sustain a weight of:
| 1. | 2.5 kg | 2. | 5 kg |
| 3. | 10 kg | 4. | 15 kg |
When a block of mass \(M\) is suspended by a long wire of length \(L,\) the length of the wire becomes \((L+l).\) The elastic potential energy stored in the extended wire is:
1. \(\frac{1}{2}MgL\)
2. \(Mgl\)
3. \(MgL\)
4. \(\frac{1}{2}Mgl\)
The bulk modulus for an incompressible liquid is:
1. zero
2. unity
3. infinity
4. between \(0\) and \(1\)
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