The correct answer is option 2: `The body has a radial acceleration x^2.r directed towards the centre of the path.` this option can be understood as follows:
Option 1: `The body has no acceleration`: This statement is incorrect. When a body moves with uniform angular velocity in a circular path, it experiences radial (centripetal) acceleration towards the center of the path.
Option 2: `The body has a radial acceleration x^2.r directed towards the centre of the path`: This statement is correct. The equation for centripetal acceleration is a = rω^2 (where ω is the angular velocity and r is the radius). Thus, the acceleration is x^2.r directed towards the center of the circular path.
Option 3: `The body has a radial acceleration 2/5.x^2.r directed away from the centre of the path`: This statement is incorrect because the acceleration is directed towards the center, not away from it.
Option 4: `The body has an acceleration x^2.r tangential to its path`: This statement is also incorrect because the acceleration due to uniform circular motion is always directed towards the center of the circle, not tangential to it.