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Q. No.A rope \(1\) cm in diameter breaks if the tension in it exceeds \(500\) N. The maximum tension that may be given to a similar rope of diameter \(2\) cm is:
1. \(500\) N
2. \(250\) N
3. \(1000\) N
4. \(2000\) N
Two wires \(A\) and \(B\) are made of the same material. The wire \(A\) has a length \(L\) and diameter \(r\) while the wire \(B\) has a length \(2L\) and diameter \(r/2.\) If the two wires are stretched by the same force, the elongation in \(A\) divided by the elongation in \(B\) is:
| 1. | \(\dfrac{1}{8}\) | 2. | \(\dfrac{1}{4}\) |
| 3. | \(4\) | 4. | \(8\) |
A wire elongates by \(1.0\) mm when a load \(W\) is hang from it. If this wire goes over a pulley and two weights \(W\) each are hung at the two ends, the elongation of the wire will be:
1. \(0.5\) m
2. \(1.0\) mm
3. \(2.0\) mm
4. \(4.0\) mm
The length of a metal wire is \(l_1\) when the tension in it is \(T_1\) and is \(l_2\) when the tension is \(T_2.\) The natural length of the wire is:
| 1. | \(\dfrac{l_{1}+l_{2}}{2}\) | 2. | \(\sqrt{l_{1} l_{2}}\) |
| 3. | \(\dfrac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}}\) | 4. | \(\dfrac{l_{1} T_{2}+l_{2} T_{1}}{T_{2}+T_{1}}\) |
The dimension \([ML^{-1}T^{-2}]\) can correspond to:
| 1. | moment of a force |
| 2. | surface tension |
| 3. | modulus of elasticity |
| 4. | coefficient of viscosity |
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 |
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