A

Step 1: To complete a full circular motion, the potential energy at height h must be converted into kinetic energy at the top of the circle.
Step 2: At the top of the circular path, the centripetal force must be provided by the gravitational force. Therefore, the condition for the block to complete the full circle is given by: \[ mgh \geq \frac{mv^2}{r} \] where v is the speed at the top of the circle.
Step 3: The minimum speed at the top required to maintain a circular path can be derived from the equation: \[ v = \sqrt{gr} \]
Step 4: Equating energies gives \[ mgh = mg \frac{r}{2} \] leading to the final relation \[ h \geq \frac{3r}{2} \]
Therefore, Option A: \[ h < \frac{5r}{2} \] holds true. Hence, A.