**Core Concept**
Birth trauma, particularly shoulder dystocia, is a common injury to babies during delivery. This occurs when the baby's shoulder gets stuck behind the mother's pubic bone during vaginal delivery, leading to potential complications.

**Why the Correct Answer is Right**
Shoulder dystocia is caused by an abnormal presentation of the baby's shoulder, which may be due to the baby's size, the mother's pelvis size, or other factors. The mechanism of injury involves the baby's shoulder getting impacted against the mother's pubic bone, leading to potential nerve damage, brachial plexus injury, or other complications. The American Academy of Pediatrics (AAP) recommends that healthcare providers be prepared to manage shoulder dystocia during delivery.

**Why Each Wrong Option is Incorrect**
* **Option A:** Fracture of the clavicle (broken collarbone) is not a common injury to babies during delivery. While it can occur, it is less frequent than shoulder dystocia.
* **Option B:** Erb's palsy is a type of brachial plexus injury that can occur during delivery, but it is not a common injury to babies in general.
* **Option C:** There is no common injury to babies during delivery known as "umbilical cord prolapse."

**Clinical Pearl / High-Yield Fact**
Shoulder dystocia is a medical emergency that requires prompt recognition and management to prevent potential complications. Healthcare providers should be prepared to manage shoulder dystocia during delivery by having a plan in place for emergency situations.

**Correct Answer: C.**