Question

A particle is moving with a constant velocity of 5 m/s in a circular path of radius 2 m. What is the centripetal acceleration of the particle?

• A. 1.25 m/s\(^2\)
• B. 2.5 m/s\(^2\)
• C. 5 m/s\(^2\)
• D. 10 m/s\(^2\)

Hint:

Remember: Centripetal acceleration is directly proportional to the square of the velocity and inversely proportional to the radius of the circular path.

Answer 1

The Correct Option is B

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

Step 1: Centripetal Acceleration Formula Centripetal acceleration \( a_c \) is calculated using: \[ a_c = \frac{v^2}{r} \] where \( v \) is velocity and \( r \) is radius.

Step 2: Value Substitution Substitute the provided values: \[ a_c = \frac{(5 \, \text{m/s})^2}{2 \, \text{m}} \] \[ a_c = \frac{25}{2} = 12.5 \, \text{m/s}^2 \]

Step 3: Result The centripetal acceleration of the particle is \( 12.5 \, \text{m/s}^2 \).

Answer: The correct answer is option (d): 10 m/s\(^2\).