**Core Concept**
The depolarization in hair cells of the organ of Corti is a critical event in the auditory pathway, leading to the transmission of sound signals to the brain. It is mediated by the movement of ions across the cell membrane, specifically the opening of mechanically gated ion channels.

**Why the Correct Answer is Right**
The depolarization in hair cells occurs due to the movement of the stereocilia, which are embedded in the overlying tectorial membrane. As sound waves cause the fluid in the cochlea to vibrate, the stereocilia bend, opening mechanically gated ion channels. This leads to an influx of potassium ions (K+) into the hair cell, causing depolarization. The depolarization of the hair cell opens voltage-gated calcium channels, allowing an influx of calcium ions (Ca2+), which in turn triggers the release of neurotransmitters.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because the depolarization in hair cells is not primarily due to the movement of sodium ions (Na+).
* **Option B:** This option is incorrect because the depolarization in hair cells is not a result of the opening of ligand-gated ion channels.
* **Option D:** This option is incorrect because the depolarization in hair cells is not a result of the opening of voltage-gated potassium channels.

**Clinical Pearl / High-Yield Fact**
It is essential to remember that the movement of the stereocilia in hair cells is the initial step in the auditory pathway, leading to the depolarization of the hair cell and the transmission of sound signals to the brain.

**Correct Answer:** C. Opening of mechanically gated ion channels