When a metal wire is stretched by a load, the fractional change in its volume \(\frac{\Delta V}{V}\) is proportional to:
1. \(\frac{\Delta l}{l}\)
2. \(\left(\frac{\Delta l}{l}\right)^{2}\)
3. \(\sqrt{\Delta l/ l}\)
4. none of these
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. \(\dfrac{l_{1} T_{2}+l_{2} T_{1}}{T_{2}+T_{1}}\)
A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break:
1. | when the mass is at the highest point |
2. | when the mass is at the lowest point |
3. | when the wire is horizontal |
4. | at an angle of \(\cos^{-1}\left(\frac{1}{3}\right)\) from the upward vertical |
When a metal wire elongates by hanging a load on it, the gravitational potential energy decreases.
1. | This energy completely appears as the increased kinetic energy of the block. |
2. | This energy completely appears as the increased elastic potential energy of the wire. |
3. | This energy completely appears as heat. |
4. | None of the above. |
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 |
A heavy uniform rod is hanging vertically from a fixed support. It is stretched by its own weight. The diameter of the rod is:
1. | smallest at the top and gradually increases down the rod. |
2. | largest at the top and gradually decreases down the rod. |
3. | uniform everywhere. |
4. | maximum in the middle. |
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
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. | \(8\) |
1. | \(10\) kg | 2. | \(20\) kg |
3. | \(40\) kg | 4. | \(80\) kg |