Inertia of a rectangular section of width and depth about an axis passing the moment of through C.G. and parallel to its width is A. $$\frac{{{\text{B}}{{\text{D}}^2}}}{6}$$ B. $$\frac{{{\text{B}}{{\text{D}}^3}}}{6}$$ C. $$\frac{{{\text{B}}{{\text{D}}^3}}}{{12}}$$ D. $$\frac{{{{\text{B}}^2}{\text{D}}}}{6}$$

The correct answer is A. $\frac{{{\text{B}}{{\text{D}}^2}}}{6}$.

The moment of inertia of a rectangular section of width $B$ and depth $D$ about an axis passing through the centroid and parallel to its width is given by the following formula:

$$I = \frac{{{\text{B}}{{\text{D}}^2}}}{6}$$

where:

• $I$ is the moment of inertia
• $B$ is the width of the rectangle
• $D$ is the depth of the rectangle

The moment of inertia is a measure of the resistance of an object to changes in its rotation. The larger the moment of inertia, the more resistant the object is to rotation.

The moment of inertia of a rectangular section is calculated by multiplying the area of the section by the square of the distance from the centroid to the axis of rotation. In this case, the distance from the centroid to the axis of rotation is equal to the depth of the rectangle, $D$.

The area of a rectangular section is given by the following formula:

$$A = B \times D$$

Therefore, the moment of inertia of a rectangular section of width $B$ and depth $D$ about an axis passing through the centroid and parallel to its width is given by the following formula:

$$I = \frac{{{\text{B}}{{\text{D}}^2}}}{6}$$