# a particle in uniform circular motion completes 2 and half revelutions in time t.the magnitude of the average vel in this time interval is,      i got the ans as  5 *22/7*R/T .but  the ans is given as 2R/T

Rajdeep
231 Points
3 years ago
HELLO THERE!

The question is relatively simple, but a bit conceptual!!

Concepts required are:

=> Average  Velocity = Total displacement / Total time taken in achieving it.
=> When a body starts a circular motion and end up stopping in the position from where it started (initial position), its displacement is ZERO.

Now, let’s analyze the given question:

Completing a revolution means, Coming back to the same point from where the particle started. Hence, when a body completes one revolution, its net displacement is zero.
It is given that the body completes 2.5 revolutions in time T.

After completing 1 revolution, displacement = 0.
After completing the 2nd revolution, displacement = 0 (again).
But, for the next 0.5th revolution, displacement is not equal to zero, as this time, the body is not completing the full circle.

For the next 0.5 revolution, the particle completes the semi-circular path (Travelling only half the circle). For this, the distance from the starting point to his end point (displacement) is equal to the diameter of the circle, which is 2R (since radius of the circle is R).

So, we get the total displacement to be 2R in time T, and since

Average velocity = Total displacement / Time,

Average Velocity = $\dpi{100} \frac{2R}{T}$

THANKS!