The correct answer is $\boxed{\text{B}. D = 0.775 a}$.
The bearing capacity of soil is the maximum load that a soil can support per unit area. The projection of plain concrete footing from walls is the distance that the footing extends beyond the wall. The depth of footing is the distance from the top of the footing to the bottom of the footing.
The formula for the depth of footing is $D = \frac{q}{B}$, where $q$ is the bearing capacity of soil, $B$ is the projection of plain concrete footing from walls, and $D$ is the depth of footing.
In this case, $q = 10 \text{ tonnes}/\text{cm}^2$ and $B = a \text{ cm}$. Therefore, the depth of footing is $D = \frac{10 \text{ tonnes}/\text{cm}^2}{a \text{ cm}} = 0.775 a$.
Option A is incorrect because it is too small. Option C is incorrect because it is too large. Option D is incorrect because it is not a valid formula for the depth of footing.