Question

A particle moves with a constant speed of 4 m/s in a circular path of radius 2 m. What is its centripetal acceleration?

• A. 8 m/s\(^2\)
• B. 4 m/s\(^2\)
• C. 16 m/s\(^2\)
• D. 2 m/s\(^2\)

Hint:

Centripetal acceleration always points toward the center of the circular path and depends on the square of the speed and inversely on the radius. Double-check units to ensure correctness.

Answer 1

The Correct Option is A

Step 1: Identify the formula for centripetal acceleration.
The centripetal acceleration \( a_c \) for an object moving in a circular path with constant speed is given by: \[ a_c = \frac{v^2}{r}, \] where \( v \) is the speed of the particle and \( r \) is the radius of the circular path.
Step 2: Substitute the given values into the formula.
The problem provides:
- Speed \( v = 4 \, \text{m/s} \),
- Radius \( r = 2 \, \text{m} \).
\[ a_c = \frac{(4)^2}{2}. \]
Step 3: Perform the calculation step-by-step. First, compute the square of the speed: \[ (4)^2 = 16. \] Then divide by the radius: \[ a_c = \frac{16}{2} = 8 \, \text{m/s}^2. \]
Step 4: Verify the result.
The units are consistent (\( \text{m}^2/\text{s}^2 \div \text{m} = \text{m/s}^2 \)), and the value 8 m/s\(^2\) aligns with the options provided, confirming the calculation.