A particle is moving along a circle suchthat it completes one revolution in 40seconds. In 2 minutes 20 seconds, theratio |𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡|𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 is

First, let's understand the terms in the question:

1. Displacement: It is the shortest distance from the initial to the final position of a point. Thus, it is a vector quantity with both magnitude and direction. For a particle moving in a circle, after one complete revolution, the displacement is zero because the initial and final positions are the same.

2. Distance: It is the total path covered by a particle. For a particle moving in a circle, the distance after one complete revolution is the circumference of the circle.

The particle completes one revolution in 40 seconds. In 2 minutes 20 seconds, which is 140 seconds, the particle would complete 140/40 = 3.5 revolutions.

Now, let's calculate the displacement and distance:

1. Displacement: After every complete revolution, the displacement is zero. So, after 3 complete revolutions, the displacement is still zero. For the 0.5 revolution, the displacement is the diameter of the circle. But since we are asked for the absolute value of displacement, we don't need to worry about the direction. So, the displacement is the diameter of the circle.

2. Distance: After 3.5 revolutions, the distance covered is 3.5 times the circumference of the circle.

The ratio of displacement to distance is therefore (diameter of the circle) / (3.5 times the circumference of the circle).

Since the diameter is twice the radius (d = 2r) and the circumference is 2π times the radius (C = 2πr), the ratio simplifies to (2r) / (3.5 * 2πr) = 1 / (3.5π).

So, the ratio of displacement to distance is 1 / (3.5π).