Question

A particle is moving with a constant velocity of \( 5 \, \text{m/s} \) in a circular path of radius \( 2 \, \text{m} \). What is the centripetal acceleration of the particle?

• A. \( 1.25 \, \text{m/s}^2 \)
• B. \(12.5 \, \text{m/s}^2 \)
• C. \( 5 \, \text{m/s}^2 \)
• D. \( 10 \, \text{m/s}^2 \)

Hint:

Remember: The centripetal acceleration depends on both the velocity of the particle and the radius of the circular path. It increases with the square of velocity and decreases with the radius.

Answer 1

The Correct Option is B

The following data is provided:

• Particle velocity: \( v = 5 \, \text{m/s} \)
• Circular path radius: \( r = 2 \, \text{m} \)

Step 1: State the centripetal acceleration formula

Centripetal acceleration is calculated using: \[ a_c = \frac{v^2}{r} \]

Step 2: Insert provided values into the formula

\[ a_c = \frac{(5)^2}{2} = \frac{25}{2} = 12.5 \, \text{m/s}^2 \]

Conclusion:

The particle's centripetal acceleration is \( 12.5 \, \text{m/s}^2 \).