Question

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

• A. 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).
• B. The centripetal acceleration is greater for a gentle curve than that for a sharp curve.
• C. The centripetal acceleration is the same for both, the gentle and sharp curves.
• D. The centripetal acceleration causes the object to slow down.

Answer 1

The correct option is A 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).

The centripetal acceleration is greater for the sharp curve (i.e for a curve of a smaller radius) than for the gentle curve (i.e for a curve of a larger radius). This is because ;

Centripetal Acceleration, $a_c$ = $\frac{v^2}{r}$.

Here, the speed is constant. If the speed $\left(v\right)$ doesn't change, then, if the radius ( r ) has a bigger value (as in the case of a gentle curve), the centripetal acceleration ($a_c$) will be smaller compared to a radius of smaller value (as seen in a sharper curve) which we can seen from the above equation.