Question

The curvature of a circle of radius 'a' is

• A. $\frac{1}{a}$
• B. $a$
• C. $a^2$
• D. $\frac{1}{a^2}$

Hint:

A larger circle bends more slowly and thus has a smaller curvature, whereas a smaller circle bends sharply and has a larger curvature.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Curvature ($\kappa$) is a geometric measure of how quickly a curve changes direction at a point.

Step 2: Detailed Explanation:
By definition, the curvature of a circle is constant at every point along its perimeter.
It is mathematically defined as the reciprocal of the radius of the circle:
\[ \kappa = \frac{1}{R} \]
Here, the radius is given as $a$.
Therefore, the curvature of the circle of radius $a$ is $\frac{1}{a}$.

Step 3: Final Answer
The correct option is (A).