**Core Concept**
The most common fractures in post-menopausal women, especially after a fall, are related to osteoporosis and the distribution of bone density. Post-menopausal women are at a higher risk of osteoporosis due to the decrease in estrogen levels, which affects bone mineral density.

**Why the Correct Answer is Right**
The most common fracture in post-menopausal women who fall is a **vertebral compression fracture**. This type of fracture occurs when the vertebral body collapses due to the loss of bone density, often as a result of osteoporosis. The decreased bone mineral density makes the spine more susceptible to compression fractures, especially in the thoracic and lumbar regions. This type of fracture is often silent, meaning it may not cause immediate symptoms, but can lead to chronic back pain, loss of height, and a hunched posture.

**Why Each Wrong Option is Incorrect**
**Option A:** **Colles' fracture** is a common fracture in the distal radius, typically seen in older adults after a fall onto an outstretched hand. While it is possible, it is not the most common fracture in post-menopausal women after a fall.

**Option B:** **Hip fracture** is a significant concern in post-menopausal women, especially after a fall. However, it is not the most common fracture in this population.

**Option C:** **Rib fracture** can occur after a fall, especially in older adults with osteoporosis. However, it is not the most common fracture in post-menopausal women.

**Clinical Pearl / High-Yield Fact**
In post-menopausal women, vertebral compression fractures are often asymptomatic, and diagnosis may be delayed until complications arise, such as chronic back pain or loss of height. A thorough clinical evaluation, including a careful history and physical examination, is essential to identify these fractures early.

**Correct Answer:** C.