Question

The ratio of displacement to distance is
$\left( A \right)$ Always less than one
$\left( B \right)$ Always greater than one
$\left( C \right)$ Always equal to one
$\left( D \right)$ Either less than or equal to one.

Answer 1

To solve this problem, we have to know about the distance and the displacement. We know that, Distance is a mathematical estimation of how far separated items or focuses are. In material science or ordinary utilization, distance may allude to an actual length or an assessment dependent on different rules.

Complete step by step answer:
We know that the distance is the actual length of the path travelled between the initial point and final point or position of that moving body. And we also know that the displacement is the linear distance between the initial position and the final position of that moving body.
Now, we all know that a straight line drawn between two points is of least length among all curves joining the two, so the linear distance between two points is the least length of path to be travelled between two points. So, we can say, that distance when it is shortest, becomes displacement. Otherwise, the distance is greater than the displacement.
So, we can conclude that the ratio of displacement to distance is less than or equal to one.
Hence option $\left( D \right)$ is the correct answer.

Note:
We can get confused between distance and displacement but we have to know perfectly about these two and have to keep those differences in our mind to solve these kinds of problems. The S.I unit of distance is meter. And the S.I unit of displacement is also meter. But distance is a scalar quantity that only consists of magnitude whereas displacement is a vector quantity that means that it consists of magnitude as well as direction. So, we do not have to be confused about this.