**Core Concept**
The pharyngeal arches are crucial structures in embryonic development, giving rise to various craniofacial and neck tissues. The cartilaginous components of these arches eventually form the cartilaginous models of the adult head and neck skeleton. Each pharyngeal arch has a distinct set of cartilaginous, muscular, and nervous components that develop into specific adult structures.

**Why the Correct Answer is Right**
The second pharyngeal arch, also known as the hyoid arch, primarily contributes to the formation of the styloid process, the stylohyoid ligament, and the lesser cornu of the hyoid bone. The cartilage of the second arch is a key component in the development of these structures. The cartilage eventually ossifies and gives rise to the adult bony components. The second arch is innervated by the facial nerve (cranial nerve VII) and is associated with the development of the muscles of facial expression.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is likely referring to the first pharyngeal arch, which primarily contributes to the formation of the mandible, maxilla, zygomatic bone, and other structures of the upper jaw. This is incorrect because the question specifically asks about the second arch.
**Option B:** This option is likely referring to the third pharyngeal arch, which primarily contributes to the formation of the greater cornu and the body of the hyoid bone. This is incorrect because the question specifically asks about the second arch.
**Option C:** This option is likely referring to the fourth pharyngeal arch, which primarily contributes to the formation of the laryngeal cartilages. This is incorrect because the question specifically asks about the second arch.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that the pharyngeal arches are not strictly sequential in their development, and there can be some overlap between arches. Additionally, abnormalities in pharyngeal arch development can lead to congenital anomalies such as cleft palate or facial asymmetry.

**Correct Answer:** B. The cartilage of the second arch is primarily associated with the development of the styloid process, the stylohyoid ligament, and the lesser cornu of the hyoid bone.