**Core Concept**
The detection of free air in the peritoneal cavity, often indicative of a perforated viscus, is a critical diagnostic finding that requires prompt recognition. This condition necessitates immediate surgical intervention to prevent peritonitis and other complications.

**Why the Correct Answer is Right**
The correct investigation for detecting free air in the peritoneal cavity is a chest X-ray, specifically a lateral decubitus view. This radiographic technique involves positioning the patient on their side, allowing the free air to rise and collect under the diaphragm. The lateral decubitus view is particularly useful as it helps to visualize the air bubbles that may not be visible on an upright chest X-ray. The presence of free air under the diaphragm is a classic sign of a perforated viscus.

**Why Each Wrong Option is Incorrect**
**Option A:** A CT scan, while highly sensitive for detecting free air, is not the first-line investigation due to its higher cost and radiation exposure. It is usually reserved for patients who are unstable or have complex abdominal pathology.
**Option B:** An ultrasound may be useful for detecting free fluid in the peritoneal cavity but is not as sensitive for detecting free air. It is also operator-dependent and may require expertise.
**Option C:** An abdominal X-ray can be used to detect free air, but a lateral decubitus view is more sensitive and specific for this purpose.

**Clinical Pearl / High-Yield Fact**
The presence of free air under the diaphragm on a chest X-ray is a classic sign of a perforated viscus, and a lateral decubitus view is the most sensitive radiographic technique for detecting this condition.

**Correct Answer: C. Abdominal X-ray (Lateral decubitus view)**