Question

A particle is moving in a circle of radius \( R \) with constant speed \( V \). The magnitude of average acceleration after half revolution is

• A. \( \frac{2V^2}{\pi R} \)
• B. \( \frac{2\pi V^2}{R^2} \)
• C. \( \frac{2V}{\pi R^2} \)
• D. \( \frac{2R}{\pi V} \)

Hint:

In circular motion, always consider the change in direction as well as the magnitude when calculating acceleration.

Answer 1

The Correct Option is A

Step 1: Understanding the problem.
The particle is moving in a circular path, and we are asked to calculate the magnitude of the average acceleration after half a revolution. The formula for average acceleration in circular motion is: \[ a = \frac{\Delta v}{\Delta t} \] where \( \Delta v \) is the change in velocity and \( \Delta t \) is the time taken for half the revolution.
Step 2: Calculation.
The change in velocity after half a revolution is the difference between the initial and final velocity vectors. Since the particle has moved half a revolution, the angle between the two velocity vectors is \( 180^\circ \), and the magnitude of the average acceleration is: \[ a = \frac{2V^2}{\pi R} \]
Step 3: Conclusion.
Thus, the correct answer is (A) \( \frac{2V^2}{\pi R} \).