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:

A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break:

When a metal wire elongates by hanging a load on it, the gravitational potential energy decreases.

The dimension \([ML^{-1}T^{-2}]\) can correspond to:

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,

Choose the correct option:

A heavy uniform rod is hanging vertically from a fixed support. It is stretched by its own weight. The diameter of the rod is:

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: