Question

What is the formula for centripetal acceleration?

• A. \(a = \frac{v}{r}\)
• B. \(a = \frac{v^2}{r}\)
• C. \(a = vr\)
• D. \(a = \frac{r}{v^2}\)

Hint:

In uniform circular motion, centripetal acceleration always points toward the center of the circle and depends on the square of velocity.

Answer 1

The Correct Option is B

Concept: Centripetal acceleration is the acceleration experienced by an object moving in a circular path. It always acts towards the center of the circular path and keeps the object moving along the curved trajectory. :contentReference[oaicite:0]{index=0}

Step 1: Understanding circular motion. When an object moves in a circle with constant speed \(v\), its direction continuously changes. This change in direction produces an acceleration directed towards the center of the circle.

Step 2: Expression for centripetal acceleration. If \(v\) is the velocity of the object and \(r\) is the radius of the circular path, the centripetal acceleration is given by: \[ a = \frac{v^2}{r} \]

Step 3: Conclusion. Thus, the formula for centripetal acceleration is \(a = \frac{v^2}{r}\).