To solve this problem, we need to analyze the given statements:$\newline \bullet$Statement I: During $G_0$ phase of the cell cycle, the cell is metabolically inactive.$\newline \bullet$Statement II: The centrosome undergoes duplication during the S phase of interphase.$\newline$Let's break down each statement:$\newline \bullet$Statement I:$\newline$ - The $G_0$ phase is a resting phase where the cell is not actively preparing to divide.$\newline$ - However, cells in $G_0$ are not metabolically inactive; they perform normal cellular functions.$\newline$ - Therefore, Statement I is incorrect.$\newline \bullet$Statement II:$\newline$ - The S phase of interphase is when DNA replication occurs.$\newline$ - During this phase, the centrosome also duplicates to prepare for cell division.$\newline$ - Therefore, Statement II is correct.$\newline$Based on this analysis:$\newline \bullet$Statement I is incorrect, but Statement II is correct.$\newline$Thus, the correct answer is Option 4: Statement I is incorrect but Statement II is correct.