Question

A particle comes round a circle of radius 1 m once. The time taken by it is 10 sec. The average velocity of motion is
A. \[0.2\pi \,m/s\]
B. \[2\pi \,m/s\]
C. \[2\,m/s\]
D. Zero

Answer 1

Hint: The average velocity of motion is the ratio of net displacement and the total time of journey. The net displacement is the change in position of the body. When the body returns to the same position after the journey then there is no change in the position of the body.

Formula used:
\[\overrightarrow {{v_{av}}} = \dfrac{{\overrightarrow {\Delta x} }}{{\Delta t}}\]
Here \[\overrightarrow {\Delta {v_{av}}} \] is the average velocity, \[\overrightarrow {\Delta x} \] is the net displacement and \[\Delta t\] is the total time of journey.

Complete step by step solution:
It is given that the particle comes around a circle once in 10 sec. When the particle comes to the same position after completing one revolution then the final position of the particle coincides with the initial position. The radius of the circle around which the particle is moving is given as 1 metre.

As we know that linear displacement is the change in position, so the net linear displacement of the particle is zero because the initial position is the same as the final position.
\[\overrightarrow {\Delta x} = 0m\]
The time taken to complete one revolution around a circle is 10 sec.
\[\Delta = 10\sec \]

So, using the average velocity formula, the average velocity of the particle during the journey will be,
\[\overrightarrow {{v_{av}}} = \dfrac{{0m}}{{10\sec }}\]
\[\therefore \overrightarrow {{v_{av}}} = 0\,m/s\]
Hence, the average velocity of the particle during this 10 sec of the journey is zero.

Therefore, the correct option is D.

Note: During the complete revolution the net distance is non-zero and it is equal to the circumference of the circular path. So, when it is asked to find the average speed then we calculate it as the ratio of the net distance travelled during the journey to the time taken to complete the journey. As the net distance covered is non-zero, so the average speed is not zero.