The correct answer is option 'D' (r^5).

Explanation:
- Circular orbit: A circular orbit is a path followed by a particle under the influence of a central force that is directed towards a fixed point on the circle. This force acts as a centripetal force, keeping the particle in its circular path.
- Inverse proportionality: When two quantities are inversely proportional, it means that as one quantity increases, the other quantity decreases, and vice versa. Mathematically, if two quantities A and B are inversely proportional, their relationship can be expressed as A ∝ 1/B or A = k/B, where k is a constant.

Now, let's consider the central force acting on the particle in the circular orbit and its relationship with the distance from the fixed point on the circle (r).

- As the particle moves away from the fixed point, the force acting towards the fixed point decreases.
- From Newton's law of universal gravitation, the force between two masses is inversely proportional to the square of the distance between them. However, in this case, the force is not necessarily gravitational, but it follows a similar pattern.
- The force acting on the particle can be expressed as F ∝ 1/r^n, where n is a constant.

To determine the value of n, we can analyze the motion of the particle in the circular orbit:
- The centripetal force required to keep the particle in its circular path is provided by the central force. This centripetal force is given by F = m(v^2/r), where m is the mass of the particle and v is its velocity.
- Equating the expressions for the force, we have m(v^2/r) = F = 1/r^n.
- Rearranging the equation, we get v^2 = r^(n-2).
- Since the particle is moving in a circular orbit, its velocity can be expressed as v = ωr, where ω is the angular velocity.
- Substituting this expression into the equation, we have (ωr)^2 = r^(n-2).
- Simplifying, we get ω^2 = r^(n-4).

From this equation, we can conclude that n-4 must be equal to 2. Therefore, n = 6.

However, we are looking for the relationship between the force and the distance, which means n should be 5 (since F ∝ 1/r^n). Therefore, the correct answer is option 'D' (r^5).