The figure shows two cylindrical rods whose centers of mass are marked as $A$ and $B$. The line $AB$ divides the region into two parts: one containing point $O$ (region $1$) and the other containing point $O'$ (region $2$). Choose the correct option regarding the center of mass of the combined system.

• A
  The center of mass of the system lies in region $1$.
• B
  The center of mass of the system lies in region $2$.
• C
  The center of mass of the system lies on line $AB$.
• D
  The center of mass of the system may lie in region $1$ or region $2$ depending on the mass of the rods.