Question

If the non-Uniform loading is of the type of parabola then for calculating the moment of inertia for areas inclined at an axis?

(a) The net load will not be formed as all the forces will be cancelled

(b) The net force will act the centre of the parabola

(c) The net force will act on the base of the loading horizontally

(d) The net force will act at the centroid of the parabola

I have been asked this question in exam.

Origin of the question is Moments of Inertia for an Area About Inclined Axis in chapter Moments of Inertia of Engineering Mechanics

Answer 1

The correct answer is (d) The net force will act at the centroid of the parabola

For explanation: The net force will act at the centroid of the parabola. Whether it be a parabola or the cubic curve the centroid is the only point at which the net force act. Force can’t be acted horizontally if the loading is vertical. Hence whatever be the shape of the loading, the centroid is the point of action of net force. Thus the use of centroid.