Option 4 correctly represents the acceleration of a particle moving in a circular path of radius r at a constant speed v.

In a circular motion, the acceleration of the particle is directed towards the center of the circle, and its magnitude is given by the equation a = v^2 / r, where v is the velocity of the particle and r is the radius of the circle.

Option 1 shows a constant non-zero acceleration, which does not match the characteristics of a particle moving in a circular path at a constant speed.

Option 2 shows an increasing acceleration, which is incorrect because the acceleration in a circular motion remains constant.

Option 3 shows a decreasing acceleration, which is also incorrect because the acceleration in a circular motion remains constant.

Option 4 correctly shows the acceleration decreasing as the radius of the circle increases. This is because the equation for acceleration in circular motion (a = v^2 / r) shows that the acceleration is inversely proportional to the radius.