Question

Calculate the centripetal acceleration of a particle moving in a circle of radius \(5\,\text{m}\) with a velocity of \(20\,\text{m/s}\).

• A. \(80 \,\text{m/s}^2\)
• B. \(40 \,\text{m/s}^2\)
• C. \(100 \,\text{m/s}^2\)
• D. \(160 \,\text{m/s}^2\)

Hint:

In circular motion problems, always remember the centripetal acceleration relation \(a = \frac{v^2}{r}\). Increasing velocity increases acceleration rapidly because velocity is squared.

Answer 1

The Correct Option is A

Concept:
For a particle moving in a circular path, the acceleration directed toward the center of the circle is called centripetal acceleration. It depends on the velocity of the particle and the radius of the circular path. \[ \text{Centripetal acceleration} = \frac{v^2}{r} \] :contentReference[oaicite:0]{index=0}

Step 1: Write the given values from the question. \[ v = 20\,\text{m/s}, \qquad r = 5\,\text{m} \]

Step 2: Substitute the values into the centripetal acceleration formula. \[ a = \frac{v^2}{r} \] \[ a = \frac{(20)^2}{5} \]

Step 3: Calculate the value. \[ a = \frac{400}{5} = 80\,\text{m/s}^2 \] Hence, the centripetal acceleration of the particle is: \[ \boxed{80\,\text{m/s}^2} \]