Question

Calculate the centripetal acceleration of a particle moving in a circle of radius \(5\,\text{m}\) with a velocity of \(20\,\text{m/s}\).

• A. \(80 \,\text{m/s}^2\)
• B. \(40 \,\text{m/s}^2\)
• C. \(100 \,\text{m/s}^2\)
• D. \(160 \,\text{m/s}^2\)

Hint:

In circular motion problems, always remember the centripetal acceleration relation \(a = \frac{v^2}{r}\). Increasing velocity increases acceleration rapidly because velocity is squared.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the centripetal acceleration of an object undergoing uniform circular motion.
Centripetal acceleration is the acceleration directed towards the center of the circular path, which changes the direction of the velocity vector.
Step 2: Key Formula or Approach:
The formula for centripetal acceleration (\(a_c\)) in terms of linear velocity (\(v\)) and radius (\(r\)) is:
\[ a_c = \frac{v^2}{r} \]
Step 3: Detailed Explanation:
Given values:
Linear velocity, \(v = 20\,\text{m/s}\)
Radius of the circle, \(r = 5\,\text{m}\)
Substituting these values into the formula:
\[ a_c = \frac{(20)^2}{5} \]
\[ a_c = \frac{400}{5} \]
\[ a_c = 80\,\text{m/s}^2 \]
Step 4: Final Answer:
The centripetal acceleration of the particle is \(80\,\text{m/s}^2\).