Step 1: Understanding the Concept:
The question asks to identify the specific cellular organelle that is primarily responsible for energy production in eukaryotic cells.
Step 2: Key Formula or Approach:
The approach is to evaluate the primary biological function of each listed organelle and identify which one is responsible for generating cellular energy in the form of ATP.
Step 3: Detailed Explanation:
Mitochondria are double-membrane-bound organelles found in most eukaryotic organisms.
They generate most of the cell's supply of adenosine triphosphate (ATP), which is used as a source of chemical energy.
Because of this crucial role in cellular respiration and energy generation, they are popularly referred to as the ''powerhouse of the cell''.
Let us review the other options for clarity.
The nucleus contains the genetic material and controls cellular activities.
Ribosomes are the cellular machinery responsible for protein synthesis.
The Golgi apparatus is involved in modifying, sorting, and packaging proteins for secretion.
Step 4: Final Answer:
Therefore, the correct organelle is Mitochondria.