The correct answer is option 'D' - a parabola.

Explanation:
A cantilever beam is a beam that is supported only at one end and is free at the other end. When a uniform load is applied to a cantilever beam, the bending moment diagram is a graphical representation of the bending moments at different points along the beam.

The shape of the bending moment diagram for a uniform cantilever beam carrying a uniformly distributed load over its length is a parabola. This can be explained using the following points:

1. Bending Moment Distribution: The bending moment at any point along the beam is a function of the load and the distance from the support. For a uniformly distributed load, the bending moment is maximum at the fixed end (support) and decreases linearly towards the free end.

2. Shape of the Bending Moment Diagram: The bending moment diagram is a plot of the bending moments at different points along the beam. Since the bending moment decreases linearly from the fixed end to the free end, the shape of the diagram is a curve. The curve is concave upwards, forming a parabola.

3. Mathematical Representation: The equation of the bending moment diagram for a uniformly distributed load on a cantilever beam can be derived using the principles of statics and mechanics of materials. The equation is given by M(x) = (wLx - wx^2/2), where M(x) is the bending moment at a distance x from the fixed end, w is the uniformly distributed load, and L is the length of the beam.

4. Graphical Representation: When the equation of the bending moment diagram is plotted on a graph, it forms a parabolic curve. The vertex of the parabola represents the maximum bending moment at the fixed end, and the end of the parabola represents the zero bending moment at the free end.

Therefore, the shape of the bending moment diagram for a cantilever beam carrying a uniformly distributed load is a parabola. This parabolic shape represents the variation of bending moments along the beam and provides valuable information for designing and analyzing the beam's structural integrity.

As we know bending moment is zero at the ends and in uniformly varying load on cantilever beam first the bending moment increases from starting point up to a point and decrease after that point to endpoint it is a parabola