Question

A particle moves with constant speed v along a circular path of radius r and completes the circle in time T. The acceleration of the particle is

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

Hint:

Centripetal acceleration can be expressed in terms of v and T.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
\(a = v^2/r\) and \(v = 2\pi r/T\).
Step 2: Detailed Explanation:
\(r = vT/2\pi\)
\(a = v^2/(vT/2\pi) = 2\pi v/T\)
Step 3: Final Answer:
Acceleration is \(\frac{2\pi v}{T}\).