A particle covers an angle of 120¡ã while moving along the circumference of a circle. Find distance and displacement.

What is the answers

To find the distance and displacement of a particle moving along the circumference of a circle, we need to know the radius of the circle.

Let's assume the radius of the circle is 'r'.

To calculate the distance covered, we can use the formula for the circumference of a circle:

Circumference = 2πr

In this case, the particle covers an angle of 120 degrees, which is one-third of a full circle (360 degrees). Therefore, the distance covered is one-third of the circumference:

Distance = (1/3) * Circumference = (1/3) * 2πr = (2π/3) * r

Now, let's calculate the displacement. Displacement is a vector quantity that represents the change in position of an object.

The displacement can be calculated by finding the straight line distance between the initial and final positions of the particle. Since the particle covers an angle of 120 degrees, it moves along an arc of the circle.

To find the displacement, we can use the formula:

Displacement = 2r * sin(angle/2)

Here, the angle is 120 degrees, so:

Displacement = 2r * sin(120/2) = 2r * sin(60) = 2r * (√3/2) = √3r

Therefore, the distance covered is (2π/3) * r and the displacement is √3r.

Note: The value of 'r' is needed to calculate the exact distances and displacement.