**Core Concept**
RNA (Ribonucleic acid) is a single-stranded nucleic acid that plays a crucial role in protein synthesis, gene expression, and cellular regulation. It is a vital molecule that carries genetic information from DNA to the ribosome, where proteins are synthesized.

**Why the Correct Answer is Right**
The correct answer is that RNA is present in the cytoplasm of eukaryotic cells, where it is involved in protein synthesis. The process of protein synthesis, also known as translation, occurs on the ribosomes, which are organelles found in the cytoplasm. RNA molecules, including messenger RNA (mRNA), transfer RNA (tRNA), and ribosomal RNA (rRNA), are essential for the translation process. The cytoplasm provides a suitable environment for protein synthesis, allowing the ribosomes to access the necessary amino acids and energy sources.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because RNA is not primarily found in the nucleus, although some RNA molecules, such as snoRNA and snRNA, are involved in RNA processing and modification within the nucleus.
**Option B:** This option is incorrect because RNA is not a component of the cell membrane. While RNA molecules can be transported across the cell membrane, they are not structural components of the membrane itself.
**Option C:** This option is incorrect because RNA is not typically found in the mitochondria. While mitochondria do contain some RNA molecules, such as mitochondrial rRNA and tRNA, the majority of RNA in eukaryotic cells is found in the cytoplasm.

**Clinical Pearl / High-Yield Fact**
One important aspect of RNA is that it is highly unstable and can be rapidly degraded by various enzymes, including ribonucleases. This instability makes RNA an ideal molecule for regulating gene expression and protein synthesis, as its levels can be quickly adjusted in response to changes in cellular needs.

**Correct Answer:** C.