Centrosome duplication takes place in this phase

The correct option is S phase.

To understand why centrosome duplication occurs during this specific phase, let us break down the cell cycle events step-by-step:
1. The Cell Cycle Overview: The cell cycle is divided into Interphase (which includes G₁, S, and G₂ phases) and the M phase (Mitosis/Meiosis). Interphase is the preparatory period during which the cell grows and replicates its genetic material and organelles.
2. Centrosome Function: The centrosome is the main microtubule-organizing center (MTOC) in animal cells. It plays a critical role in organizing the mitotic spindle, which is responsible for pulling sister chromatids apart during cell division.
3. Coordinated Duplication: To ensure that a dividing cell has exactly two poles to construct a bipolar spindle, the single centrosome present in the G₁ phase must duplicate exactly once before cell division. This process is tightly coordinated with DNA replication to prevent genomic instability.
4. S Phase (Synthesis Phase) Events: The S phase is characterized by the replication of genomic DNA. In parallel with DNA replication, centrosome duplication is initiated during the late G₁ to early S phase and is completed during the S phase. Both DNA replication and centrosome duplication are triggered by the activation of the Cyclin E-CDK2 complex.
5. Subsequent Phases: Once duplicated in the S phase, the two centrosomes remain together as a single complex until the onset of the M phase (Mitosis), where they separate to form the two poles of the mitotic spindle.

Therefore, centrosome duplication takes place precisely during the S phase of the cell cycle.