Question

A particle is moving along a circular path of radius \(r\) with velocity \(v\). The magnitude of average acceleration after half revolution is

• A. \( \dfrac{3v^2}{\pi r} \)
• B. \( \dfrac{2v^2}{\pi r} \)
• C. \( \dfrac{3v^2}{2\pi r} \)
• D. \( \dfrac{v^2}{\pi r} \)

Hint:

For half revolution in circular motion, velocity change is always \(2v\).

Answer 1

The Correct Option is B

Step 1: Definition of average acceleration.
\[ a_{\text{avg}} = \frac{\Delta \vec{v}}{\Delta t} \]
Step 2: Change in velocity after half revolution.
After half revolution, velocity reverses direction. Hence,
\[ \Delta v = v + v = 2v \]
Step 3: Time taken for half revolution.
\[ \Delta t = \frac{\pi r}{v} \]
Step 4: Calculating average acceleration.
\[ a_{\text{avg}} = \frac{2v}{\pi r / v} = \frac{2v^2}{\pi r} \]
Step 5: Conclusion.
The magnitude of average acceleration is \( \dfrac{2v^2}{\pi r} \).