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

We are given the following data:

• Velocity of the particle, \( v = 5 \, \text{m/s} \)
• Radius of the circular path, \( r = 2 \, \text{m} \)

Step 1: Recall the formula for centripetal acceleration

The formula for centripetal acceleration is: \[ a_c = \frac{v^2}{r} \]

Step 2: Substitute the given values into the formula

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

Conclusion:

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