Question

A particle moves in a circle of radius 2 m with a speed of 6 m/s. What is the centripetal acceleration of the particle?

• A. 9 m/s\(^2\)
• B. 18 m/s\(^2\)
• C. 3 m/s\(^2\)
• D. 36 m/s\(^2\)

Hint:

The centripetal acceleration is always directed towards the center of the circular path and is proportional to the square of the velocity and inversely proportional to the radius.

Answer 1

The Correct Option is B

The formula for centripetal acceleration is: \[ a_c = \frac{v^2}{r} \] where: - \(v = 6 \, \text{m/s}\) (velocity) - \(r = 2 \, \text{m}\) (radius) Substituting the given values: \[ a_c = \frac{6^2}{2} = \frac{36}{2} = 18 \, \text{m/s}^2 \] Thus, the centripetal acceleration is 18 m/s\(^2\).