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.
\(\dfrac{1}{2}\)
The stress versus strain graphs for wires of two materials \(A\) and \(B\) are as shown in the figure. If \(Y_A\) \(Y_B\) are the Young's moduli of the materials, then:
| 1. | \(Y_B = 2Y_A\) | 2. | \(Y_A = Y_B\) |
| 3. | \(Y_B = 3Y_A\) | 4. | \(Y_A =3 Y_B\) |
| 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 |
| 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. | \(\frac{Er}{AR}\) |
| 1. | Breaking stress does not depend on the area of cross-section. |
| 2. | \(B_{\text {solid }}>{B}_{\text {gas }}>{B}_{\text {liquid }}\) where \(B\) is the bulk modulus. |
| 3. | Breaking load does not depend on the area of cross-section. |
| 4. | Young's modulus always decreases on decreasing the temperature. |
A wire of negligible mass and length \(2\) m is stretched by hanging a \(20\) kg load to its lower end keeping its upper end fixed. If work done in stretching the wire is \(50\) J, then the strain produced in the wire will be:
1. \(0.5\)
2. \(0.1\)
3. \(0.4\)
4. \(0.25\)
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 compressibility of water is \(4\times 10^{-5}\) per unit atmospheric pressure. The decrease in volume of \(100\) cubic centimeter of water under a pressure of \(100\) atmosphere will be:
1. \(0.4~\text{cc}\)
2. \(4\times 10^{-5}~\text{cc}\)
3. \(0.025~\text{cc}\)
4. \(0.004~\text{cc}\)
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. | \(0.03\) |
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