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

Step 1: Formula for Centripetal Acceleration The centripetal acceleration \( a_c \) is given by the formula: \[ a_c = \frac{v^2}{r} \] where: - \( v \) is the velocity, - \( r \) is the radius. 

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

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

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