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

Step 1: Understanding the Question:
The question asks for the mathematical expression of the acceleration that acts on a body moving in a circular path, directed toward the center.
Step 2: Key Formula or Approach:
In uniform circular motion, centripetal acceleration (\( a_c \)) is related to the linear velocity (\( v \)), angular velocity (\( \omega \)), and radius (\( r \)).
Basic formulas:
\[ a_c = \frac{v^2}{r} \]
\[ a_c = \omega^2 r \]
Step 3: Detailed Explanation:
When an object moves in a circle of radius \( r \) with a constant speed \( v \), its velocity vector is constantly changing direction.
This change in direction implies an acceleration.
Derived from the geometry of the motion, the magnitude of this acceleration is proportional to the square of the speed and inversely proportional to the radius of the path.
Step 4: Final Answer:
The correct formula for centripetal acceleration is \( a = \frac{v^2}{r} \).