The general expression for the B.M. of a beam of length $$l$$ is the beam carries $${\text{M}} = \frac{{{\text{w}}l}}{2} \times – \frac{{{\text{w}}{{\text{x}}^2}}}{2}$$ A. A uniformly distributed load w/unit length B. A load varying linearly from zero at one end to w at the other end C. An isolated load at mid span D. None of these

The correct answer is: A. A uniformly distributed load w/unit length.

The expression for the bending moment (BM) of a beam of length $l$ is:

$$M = \frac{wl}{2} \times – \frac{wx^2}{2}$$

where $w$ is the load per unit length and $x$ is the distance from the left end of the beam.

This expression is for a uniformly distributed load, which means that the load is evenly distributed along the length of the beam. The BM is zero at the ends of the beam, where the load is applied, and it reaches a maximum at the center of the beam.

The other options are not correct because they do not describe a uniformly distributed load. Option B describes a load that varies linearly from zero at one end to $w$ at the other end. Option C describes an isolated load at mid-span. Option D is not a valid option.