A body is revolving with a uniform speed v in a circle of radius r. The angular acceleration of the body is

The correct option is Zero.

Let's understand why the angular acceleration of the body is zero by breaking down the concepts step-by-step:

1. Understanding Uniform Circular Motion:
When a body revolves in a circular path of radius $r$ with a uniform speed $v$, the speed (magnitude of velocity) remains constant at every point of its motion.

2. Relationship between Linear Speed and Angular Speed:
The relation between the linear speed $v$ and the angular speed $\omega$ is given by the formula:
$v=r\omega$
Rearranging the formula for angular speed $\omega$:
$\omega =\frac{v}{r}$

3. Analyzing the Angular Speed:
Since the linear speed $v$ is uniform (constant) and the radius of the circle $r$ is constant, the angular speed $\omega$ must also remain constant over time.

4. Calculating Angular Acceleration:
Angular acceleration ($\alpha$) is defined as the rate of change of angular speed with respect to time:
$\alpha =\frac{d\omega }{dt}$
Since the angular speed $\omega$ is constant, its derivative with respect to time is zero:
$\alpha =0$

Therefore, the angular acceleration of the body is Zero.