The preferred option for holding an odd-shaped workpiece in a centre lathe is

The correct option is four jaw chuck.

Explanation:

In a centre lathe, different work-holding devices are used depending on the shape, size, and symmetry of the workpiece being machined:

1. Three-jaw chuck: Also known as a self-centering chuck, it has three jaws that move simultaneously. It is ideal for holding circular, hexagonal, or other regularly shaped symmetrical workpieces because it automatically centers them. However, it cannot securely or properly grip irregular or odd-shaped workpieces.

2. Four-jaw chuck: Also known as an independent chuck, it has four jaws, each of which can be moved and adjusted independently of the others. This independent movement allows the operator to set up and securely grip irregular, rectangular, unsymmetrical, or odd-shaped workpieces. It also allows for eccentric turning, where the axis of the workpiece does not align with the lathe spindle axis.

3. Live and dead centres: These are used to support long workpieces between the headstock and tailstock, rather than holding odd-shaped workpieces directly.

4. Lathe dog: A lathe dog (or carrier) is used in conjunction with driving plates and centres to transmit rotary motion from the spindle to the workpiece when machining between centres, not for holding odd-shaped workpieces.

Therefore, a four jaw chuck is the most preferred option for holding an odd-shaped workpiece on a centre lathe.