Question

A particle moves with a constant velocity of \(5\ \text{m/s}\) in a circular path of radius \(2\ \text{m}\); calculate its centripetal acceleration.

• A. \(5\ \text{m/s}^2\)
• B. \(10\ \text{m/s}^2\)
• C. \(12.5\ \text{m/s}^2\)
• D. \(25\ \text{m/s}^2\)

Hint:

Centripetal acceleration always points toward the center of the circular path and is given by \( a_c = \dfrac{v^2}{r} \).

Answer 1

The Correct Option is C

Concept: For circular motion, the centripetal acceleration is given by \[ a_c = \frac{v^2}{r} \] where \(v\) = velocity of the particle \(r\) = radius of the circular path.

Step 1: Substitute the given values. \[ v = 5\ \text{m/s}, \qquad r = 2\ \text{m} \] \[ a_c = \frac{5^2}{2} \]

Step 2: Calculate the acceleration. \[ a_c = \frac{25}{2} = 12.5\ \text{m/s}^2 \] Thus, the centripetal acceleration is \[ \boxed{12.5\ \text{m/s}^2} \]