Q. No.A student plots a graph from his readings on the determination of Young modulus of a metal wire but forgets to put the labels (figure). The quantities on X and Y-axes may be respectively,
| (a) | weight hung and length increased |
| (b) | stress applied and length increased |
| (c) | stress applied and strain developed |
| (d) | length increased and the weight hung |
Choose the correct option:
| 1. | (a) and (b) |
| 2. | (b) and (c) |
| 3. | (a), (b) and (d) |
| 4. | all of these |
| 1. | \(0.625\) mm | 2. | \(0.65\) mm |
| 3. | \(0.672\) mm | 4. | \(0.72\) mm |
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. |  |
(Given Young’s modulus of the wire \(=2\times10^{11}\) N/m2)
1. \(1\times10^{7}\) N
2. \(1.5\times10^{7}\) N
3. \(2\times10^{7}\) N
4. \(2.5\times10^{7}\) N
(Given: Young’s modulus \(Y=2\times 10^{11}\) N-m–2 and \(g=10~\text{ms}^{–2 }\) )
1. \(12\times 10^{-9}\) m
2. \(30\times 10^{-9}\) m
3. \(25\times 10^{-9}\) m
4. \(35\times 10^{-9}\) m
A wire of cross-section \(A_{1}\) and length \(l_1\) breaks when it is under tension \(T_{1};\) a second wire made of the same material but of cross-section \(A_{2}\) and length \(l_2\) breaks under tension \(T_{2}.\) A third wire of the same material having cross-section \(A,\) length \(l\) breaks under tension \(\frac{T_1+T_2}{2}.\) Then:
| 1. | \(A=\frac{A_1+A_2}{2},~l=\frac{l_1+l_2}{2}\) |
| 2. | \(l=\frac{l_1+l_2}{2}\) |
| 3. | \(A=\frac{A_1+A_2}{2}\) |
| 4. | \(A=\frac{A_1T_1+A_2T_2}{2(T_1+T_2)},~l=\frac{l_1T_1+l_2T_2}{2(T_1+T_2)}\) |
| 1. | larger in the rod with a larger Young's modulus |
| 2. | larger in the rod with a smaller Young's modulus |
| 3. | equal in both the rods |
| 4. | negative in the rod with a smaller Young's modulus |
| 1. | \(1\) | 2. | \(2\) |
| 3. | \(\sqrt 2\) | 4. | \(\dfrac12\) |
A steel wire of length \(4.7\) m and cross-sectional area \(3.0 \times 10^{-5}\) m2 is stretched by the same amount as a copper wire of length \(3.5\) m and cross-sectional area of \(4.0 \times 10^{-5}\) m2 under a given load. The ratio of Young’s modulus of steel to that of copper is:
| 1. | \(1.79:1\) | 2. | \(1:1.79\) |
| 3. | \(1:1\) | 4. | \(1.97:1\) |
Four identical hollow cylindrical columns of mild steel support a big structure of a mass of \(50,000\) kg. The inner and outer radii of each column are \(30\) cm and \(60\) cm respectively. Assuming the load distribution to be uniform, the compressional strain of each column is:
(Given, Young's modulus of steel, \(Y = 2\times 10^{11}~\text{Pa}\))
| 1. | \(3.03\times 10^{-7}\) | 2. | \(2.8\times 10^{-6}\) |
| 3. | \(7.22\times 10^{-7}\) | 4. | \(4.34\times 10^{-7}\) |
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