Introduction:
The problem involves a particle moving in a circular path with uniform speed. The goal is to find the displacement of the particle after it has described an angle of 60 degrees.

Formula:
The displacement of a particle moving on a circular path can be calculated using the formula:

Displacement = R (1-cosθ)

Where R is the radius of the circular path and θ is the angle described by the particle.

Calculation:
Given that the radius of the circular path is r and the angle described by the particle is 60 degrees, we can calculate the displacement as follows:

θ = 60 degrees = π/3 radians (since 180 degrees = π radians)

Displacement = r (1-cos(π/3))
= r (1-1/2)
= r/2

Therefore, the displacement of the particle after it has described an angle of 60 degrees is r/2.

Explanation:
When a particle moves on a circular path with uniform speed, it completes equal distances in equal intervals of time. The displacement of the particle is the straight line distance between the initial and final positions of the particle.

In the given problem, the particle has described an angle of 60 degrees on the circular path. This means that it has covered one-sixth of the circumference of the circle. The displacement of the particle can be calculated using the formula mentioned above, which gives the straight line distance between the initial and final positions of the particle.

The angle described by the particle is used to calculate the cosine of the angle, which is subtracted from 1 to get the value of (1-cosθ). This value is then multiplied by the radius of the circular path to get the displacement of the particle.

In this case, the angle described by the particle is 60 degrees, which is equivalent to π/3 radians. The value of (1-cos(π/3)) is 1/2. Therefore, the displacement of the particle is half of the radius of the circular path.

Conclusion:
The displacement of a particle moving on a circular path can be calculated using the formula: Displacement = R (1-cosθ). In the given problem, the displacement of the particle after it has described an angle of 60 degrees on a circular path of radius r with uniform speed is r/2.