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: Determine the equation for centripetal acceleration. For an object moving in a circular trajectory at a uniform velocity, centripetal acceleration \( a_c \) is calculated as: \[ a_c = \frac{v^2}{r}, \] where \( v \) signifies the particle's speed and \( r \) denotes the radius of the circular path.
Step 2: Input the provided measurements into the equation. The problem specifies:
- Velocity \( v = 4 \, \text{m/s} \),
- Radius \( r = 2 \, \text{m} \).
\[ a_c = \frac{(4)^2}{2}. \]
Step 3: Execute the calculation sequentially. Initially, square the velocity: \[ (4)^2 = 16. \] Subsequently, divide by the radius: \[ a_c = \frac{16}{2} = 8 \, \text{m/s}^2. \]
Step 4: Confirm the accuracy of the outcome. The dimensional analysis is coherent (\( \text{m}^2/\text{s}^2 \div \text{m} = \text{m/s}^2 \)), and the computed value of 8 m/s\(^2\) corresponds with the available choices, thereby validating the computation.