1. If the non-Uniform loading is of the type of parabola then for calculating the Mohr’s circle for the 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
**Option (A): The net load will not be formed as all the forces will be cancelled.**
- This statement suggests that the forces due to the parabolic loading would cancel each other out, resulting in no net load. However, this is generally not the case with parabolic loading; there typically is a resultant load and resultant moment.
**Option (B): The net force will act at the centre of the parabola.**
- This option implies that the resultant force due to the parabolic loading acts at the centroid or center of the parabola. This is a reasonable assumption because the centroid of the parabolic loading distribution is where the resultant force would theoretically act.
**Option (C): The net force will act on the base of the loading horizontally.**
- This statement suggests that the resultant force acts horizontally at the base of the parabola. However, the location where the resultant force acts is generally at the centroid of the loading distribution rather than at the base.
**Option (D): The net force will act at the centroid of the parabola.**
- This option directly states that the resultant force due to the parabolic loading acts at the centroid of the parabola. In mechanics and engineering, this is a fundamental principle: the resultant force due to a distributed loading acts at the centroid of the loading distribution.
**Correct Answer:** Option (D) - The net force will act at the centroid of the parabola.
**Explanation:**
- For parabolic loading, the intensity of the load varies, but the resultant force can be found by integrating the load distribution over the area or length where it acts.
- The centroid of the parabolic loading distribution is where the resultant force would act if it were concentrated as a single force.
- When calculating Mohr's circle for inertia, understanding where the resultant force acts is crucial for determining the principal moments of inertia and their orientations relative to the centroidal axes of the loading.
Therefore, option (D) correctly identifies the location where the resultant force due to parabolic loading would act, which is essential for subsequent calculations involving Mohr's circle for inertia.