An object moves in a circular path with a constant speed

• GP Motion Force

An object moves in a circular path with a constant speed. Which one of the following statements is correct?

1. The centripetal acceleration of the object is smaller for a gentle curve (i.e., curve of larger radius) than that for a sharp curve (i.e., curve of smaller radius).
2. The centripetal acceleration is greater for a gentle curve than that for a sharp curve.
3. The centripetal acceleration is the same for both, the gentle and sharp curves.
4. The centripetal acceleration causes the object to slow down.

Answer

The centripetal acceleration is greater for the sharp curve than for the gentle curve.

Centripetal Acceleration, a_c = v²/r

The speed is constant. If the speed (v) doesn't change, then the bigger the r is, the smaller a_c will be. A gentle curve has a bigger radius than a sharp curve.

The correct option is A.