A body moving in a circular path with constant speed has variable acceleration.

Explanation:
When an object moves in a circular path with a constant speed, it always experiences acceleration towards the center of the circle. This acceleration is called centripetal acceleration and is directed radially inward. However, the magnitude of this acceleration remains constant throughout the motion.

Let's break down the explanation into headings and bullet points for clarity:

Centripetal Acceleration:
- When an object moves in a circular path, it constantly changes its direction.
- Since velocity is a vector quantity and has both magnitude and direction, a change in the direction of motion means a change in velocity.
- According to Newton's first law of motion, an object cannot change its velocity unless acted upon by an external force.
- In circular motion, this external force is provided by the centripetal force, which is directed towards the center of the circle.
- As a result, the object experiences acceleration towards the center of the circle, known as centripetal acceleration.

Constant Speed:
- The question states that the body is moving with a constant speed.
- Constant speed means that the magnitude of the velocity remains the same throughout the motion.
- However, since velocity is a vector quantity, the direction of the velocity is constantly changing in circular motion.

Variable Acceleration:
- The acceleration experienced by the body moving in a circular path is centripetal acceleration.
- The centripetal acceleration is always directed towards the center of the circle and is given by the formula: a = v^2/r, where v is the velocity and r is the radius of the circle.
- In the case of a body moving in a circular path with constant speed, the magnitude of the centripetal acceleration remains constant.
- However, since the direction of the velocity is constantly changing, the direction of the centripetal acceleration also changes.
- Therefore, the overall acceleration of the body is variable as it changes its direction along the circular path.

Hence, the correct answer is option 'D' - variable acceleration.