A particle is moving along a circular path of radius r, when it makes half a rotation, what is the ratio between its displacement and distance?
(a) 2π
(b) π
(c) π/2
(d) π/4
2r/πr = 2/π
π/2 is the ratio between its distance traveled (πr) and its displacement (2r).
how we get displacement and distance
To find the ratio between the displacement and distance of a particle moving along a circular path, we need to understand the concepts of displacement and distance.
Displacement is a vector quantity that represents the change in position of an object. It is measured in terms of magnitude and direction. In the case of circular motion, the displacement is the shortest distance between the starting and ending points, considering the direction of motion.
Distance, on the other hand, is a scalar quantity that represents the actual length of the path traveled by an object. It only takes into account the magnitude or numerical value and ignores any directional information.
When the particle completes half a rotation along the circular path, it essentially travels a distance equal to the circumference of the circle. The circumference of a circle is calculated using the formula:
Circumference = 2πr
where 'r' represents the radius of the circle.
Given that the particle makes half a rotation, which is equivalent to traveling a distance equal to the circumference, we can say that the distance traveled is 2πr.
However, the displacement of the particle when it completes half a rotation is zero because it returns to its original position.
Therefore, the ratio between the displacement and distance in this scenario can be calculated as:
Displacement/Distance = 0 / (2πr) = 0
Hence, the correct answer is not among the given options.
To determine the ratio between the displacement and distance of a particle moving along a circular path, we need to understand the concepts of displacement and distance.
Displacement refers to the change in position of an object from its initial point to its final point. It is a vector quantity and can be calculated by subtracting the initial position vector from the final position vector.
Distance, on the other hand, refers to the length of the actual path traveled by an object. It is a scalar quantity and does not depend on direction.
In this case, the particle is moving along a circular path of radius r. When it makes half a rotation, the displacement of the particle is equal to the diameter of the circle (2r). This is because the particle started at one end of the diameter and ended at the other end after half a rotation.
The distance traveled by the particle is equal to the circumference of the circle (2πr). This is because the particle traveled along the entire circumference of the circle during half a rotation.
Now, let's calculate the ratio between displacement and distance:
Ratio = Displacement / Distance
= 2r / 2πr
= 1/π
Therefore, the correct answer is (b) π. The ratio between the displacement and distance of the particle when it makes half a rotation is π.