**Core Concept**
Irritable hip, also known as transient synovitis of the hip, is a common cause of hip pain in children, typically presenting with acute onset of pain and limited mobility. The differential diagnosis of irritable hip in children involves a range of conditions that may mimic the symptoms of transient synovitis.

**Why the Correct Answer is Right**
Irritable hip is characterized by inflammation of the synovial membrane surrounding the hip joint, leading to pain, stiffness, and limited mobility. The diagnosis is often made clinically, with a thorough history and physical examination helping to distinguish it from other conditions. Conditions that may present similarly to irritable hip include Perthes disease, Legg-Calve-Perthes disease, and slipped capital femoral epiphysis.

**Why Each Wrong Option is Incorrect**
* **Option A:** This condition may present with hip pain, but it typically occurs in older children and adolescents, and is characterized by avascular necrosis of the femoral head. It is not a primary consideration in the differential diagnosis of irritable hip in younger children.
* **Option B:** This condition is a type of hip dislocation, where the femoral head is displaced from the acetabulum. It may present with hip pain and limited mobility, but is typically associated with a clear history of trauma.
* **Option C:** This is a type of bone tumor that can occur in the hip region, but is relatively rare in children. It may present with hip pain, but is not a common consideration in the differential diagnosis of irritable hip.

**Clinical Pearl / High-Yield Fact**
In children with hip pain, it's essential to consider the age of the child, as certain conditions are more common in specific age groups. For example, Perthes disease typically occurs in children between 4-10 years of age, while slipped capital femoral epiphysis often presents in adolescents.

**Correct Answer:** A.