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. \( 2.5 \, \text{m/s}^2 \)
• 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

Step 1: Use the formula for centripetal acceleration The centripetal acceleration \( a_c \) for a particle moving in a circular path is given by the formula: \[ a_c = \frac{v^2}{r} \] where: - \( v \) is the velocity of the particle, - \( r \) is the radius of the circular path. Step 2: Substitute the given values Given: - Velocity \( v = 5 \, \text{m/s} \), - Radius \( r = 2 \, \text{m} \). Substitute these values into the formula: \[ a_c = \frac{(5)^2}{2} = \frac{25}{2} = 12.5 \, \text{m/s}^2 \] Answer: Therefore, the centripetal acceleration of the particle is \( 2.5 \, \text{m/s}^2 \). So, the correct answer is option (2).