Explanation:

To understand the given statement, we need to understand the terms mentioned in it. Let's define each term first:

Bending Moment Diagram: It is a graphical representation of the bending moment variation along the length of the beam.

Flexural Rigidity: It is a measure of a beam's resistance to bending deformation under load.

Deflection: It is the displacement of a point on the beam from its original position when it is subjected to a load.

Slope: It is the angle between the tangent to the deflected beam and the horizontal axis.

Shear Force: It is the force acting perpendicular to the longitudinal axis of the beam.

Now, let's analyze the given statement:

Ratio of the area under the bending moment diagram to the flexural rigidity:

This ratio represents the total deformation (specifically, the change in slope) caused by the bending moment along the beam.

Change in slope:

The change in slope is the difference between the initial slope and the final slope of the beam when it is subjected to a load. It is measured in radians or degrees.

Thus, the given statement implies that the ratio of the area under the bending moment diagram to the flexural rigidity between any two points along a beam gives the change in slope of the beam between those two points.

This is because the bending moment diagram represents the variation of bending moment along the beam, and the flexural rigidity represents the resistance of the beam to deformation. Therefore, the ratio of these two quantities can be used to determine the amount of deformation (change in slope) that occurs between any two points along the beam.

Conclusion:

Hence, we can conclude that the correct answer is option B, i.e., the ratio of the area under the bending moment diagram to the flexural rigidity between any two points along a beam gives the change in slope.