Question

If the non-Uniform loading is of the type of parabola then for calculating the mass moment of inertia for areas?

(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 by my college professor while I was bunking the class.

My doubt stems from Mass Moment of Inertia topic in chapter Moments of Inertia of Engineering Mechanics

Answer 1

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

To elaborate: 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.