To find the distance covered by an object moving in a circular path, you need to calculate the arc length. The formula for the arc length $s$ of a circle is:

$$s=r\theta$$

where:
- $r$ is the radius of the circle
- $\theta$ is the angle in radians

First, convert the angle from degrees to radians:

$$\theta =\frac{{30}^{\circ }\times \pi }{{180}^{\circ }}=\frac{\pi }{6}$$

Now, use the formula to find the arc length:

$$s=r\times \theta$$
$$s=21\times \frac{\pi }{6}$$
$$s=21\times \frac{3.14}{6}$$
$$s\approx 21\times 0.523$$
$$s\approx 10.98$$

Rounded to the nearest meter, the distance covered is approximately 11 meters.

So, the correct answer is:

A. 11m