Question

A particle moves with a constant velocity of \(5\ \text{m/s}\) in a circular path of radius \(2\ \text{m}\); calculate its centripetal acceleration.

• A. \(5\ \text{m/s}^2\)
• B. \(10\ \text{m/s}^2\)
• C. \(12.5\ \text{m/s}^2\)
• D. \(25\ \text{m/s}^2\)

Hint:

Centripetal acceleration always points toward the center of the circular path and is given by \( a_c = \dfrac{v^2}{r} \).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The problem asks for the centripetal acceleration of a particle undergoing uniform circular motion, given its speed and the radius of its path.
Step 2: Key Formula or Approach:
The formula for centripetal acceleration (\(a_c\)) of an object moving in a circle is:
\[ a_c = \frac{v^2}{r} \] where \(v\) is the tangential speed of the particle and \(r\) is the radius of the circular path.
Step 3: Detailed Explanation:
We are given the following values from the problem statement:
- Speed of the particle, \(v = 5 \text{ m/s}\).
- Radius of the circular path, \(r = 2 \text{ m}\).
Substitute these values into the centripetal acceleration formula:
\[ a_c = \frac{(5 \text{ m/s})^2}{2 \text{ m}} \] Calculate the square of the velocity:
\[ a_c = \frac{25 \text{ m}^2/\text{s}^2}{2 \text{ m}} \] Perform the division to find the acceleration:
\[ a_c = 12.5 \text{ m/s}^2 \] Step 4: Final Answer:
The centripetal acceleration of the particle is \(12.5 \text{ m/s}^2\).