Question

A body is moving with a constant speed \(v\) in a circular path of radius \(r\). The magnitude of average velocity after half a revolution is: 

• A. \(\frac{2v}{\pi}\)
• B. \(v\)
• C. \(\frac{v}{\pi}\)
• D. zero Correct Answer: (A) \(\frac{2v}{\pi}\) Solution:

Hint:

In circular motion, average speed depends on total distance travelled, whereas average velocity depends only on displacement. After half a revolution, displacement equals the diameter of the circle.

Answer 1

The Correct Option is A

Step 1: Picture the path.
The body runs on a circle of radius $r$ at a steady speed $v$. After half a turn it lands on the point straight across the circle.

Step 2: Find the displacement.
Displacement is the straight line from start to finish. That line is the diameter of the circle.
\[ \text{Displacement} = 2r \]

Step 3: Find the time.
Half a turn covers half the circumference, which is $\pi r$. Since speed stays the same, the time is distance over speed.
\[ t = \frac{\pi r}{v} \]

Step 4: Get the average velocity.
Average velocity is displacement divided by time.
\[ v_{avg} = \frac{2r}{\pi r / v} = \frac{2v}{\pi} \]
\[ \boxed{\dfrac{2v}{\pi}} \]