**Core Concept**
The question tests the understanding of the sensitivity of cellular structures to ionizing radiation, a fundamental principle in radiotherapy. Ionizing radiation induces DNA damage, DNA strand breaks, and base damage, leading to cell death or mutations. Cellular structures with high DNA content, rapid cell division, and limited DNA repair capacity are more susceptible to radiation damage.

**Why the Correct Answer is Right**
The most sensitive structure in cells for radiotherapy is the **mitotic spindle apparatus**. This is because it contains high concentrations of DNA and is involved in rapid cell division, making it more vulnerable to radiation-induced DNA damage. The mitotic spindle apparatus is responsible for the separation of chromosomes during mitosis, and its disruption leads to genetic mutations, chromosomal aberrations, and cell death. Radiation-induced damage to the mitotic spindle apparatus is a critical factor in the efficacy of radiotherapy.

**Why Each Wrong Option is Incorrect**
* **Option A:** The **nucleus** is a sensitive structure, but it is not the most sensitive. The nucleus contains DNA, but it has a more organized and compact structure, making it less susceptible to radiation damage compared to the mitotic spindle apparatus.
* **Option B:** The **cytoplasm** is not a sensitive structure for radiotherapy. It contains various organelles and proteins, but it is not directly involved in DNA replication and repair, making it less susceptible to radiation damage.
* **Option C:** The **cell membrane** is not a sensitive structure for radiotherapy. It is a lipid bilayer that regulates cell signaling and communication, but it is not directly involved in DNA replication and repair, making it less susceptible to radiation damage.

**Clinical Pearl / High-Yield Fact**
Remember that the mitotic spindle apparatus is a critical target for radiotherapy, and its disruption leads to genetic mutations and cell death. This is why radiotherapy is often more effective in rapidly dividing cells, such as cancer cells.

**Correct Answer:** D. **Mitotic spindle apparatus**