Question

A body moves in a circle of radius \( r = 5 \, \text{m} \) with a constant speed of \( v = 10 \, \text{m/s} \). What is the centripetal acceleration of the body?

• A. \( 20 \, \text{m/s}^2 \)
• B. \( 5 \, \text{m/s}^2 \)
• C. \( 10 \, \text{m/s}^2 \)
• D. \( 2 \, \text{m/s}^2 \)

Hint:

To calculate centripetal acceleration, use the formula \( a_c = \frac{v^2}{r} \), where \( v \) is the velocity and \( r \) is the radius of the circular path.

Answer 1

The Correct Option is A

Given:

• Radius \( r = 5 \, \text{m} \)
• Speed \( v = 10 \, \text{m/s} \)

Step 1: Use the formula for centripetal acceleration

The formula for centripetal acceleration is:

\[ a_c = \frac{v^2}{r} \] where: - \( a_c \) is the centripetal acceleration, - \( v \) is the speed of the object, - \( r \) is the radius of the circular path.

Step 2: Substitute the given values into the formula

\[ a_c = \frac{(10 \, \text{m/s})^2}{5 \, \text{m}} \] \[ a_c = \frac{100}{5} = 20 \, \text{m/s}^2 \]

✅ Final Answer:

The centripetal acceleration of the body is \( \boxed{20 \, \text{m/s}^2} \).