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A body is moving along a circular path of radius r. What will be the displacement of the body when it completes half a revolution?(A) 0(B) $2r$(C) $\pi r$(D) $2\pi r$

Last updated date: 22nd Jul 2024
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Hint It is given in our question that a body is moving along a circular path of radius r. It is essential to understand that displacement is defined as the shortest distance travelled by the body undergoing this motion. Use this to find the value.

Complete Step By Step Solution
It is given that a body is moving along a circular path of given radius r. Hence , in one revolution it is said to complete a total distance r with an area of $\pi {r^2}$. In layman terms distance travelled by the object in a circular motion is said to be it’s circumference. So, when a body completes one full rotation , it is said to have covered a distance of $2\pi r$.
Now displacement is defined as the shortest path the object takes to reach a point in the reference plane. Now, it is given that the body will complete half the revolution. In a circular motion, the shortest path a body can take from its starting point has to be in a straight line, covering its radius in full. Since the body is said to have travelled only half revolution, the total displacement from the starting point is twice the radius of the circle, $2r$ and the distance travelled from the starting point is half the circumference of the circle which is $\pi r$.

Therefore the displacement of the body in half revolution is $2r$. Hence , Option (b) is the right answer.

Note In a circular motion, we calculate velocity of the body quite differently from a linear velocity. At a given instance in its circular path, the body is said to make an angle with the reference plane. This angular change is called angular displacement and the velocity undergone by the body is called angular velocity.