Moment of inertia of a rectangular section, having 'b' width and the depth 'd', about its vertical centroidal axis is-a)db3/12b)db3/3c)bd3/12d)bd3/3Correct answer is option 'A'. Can you explain this answer?

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Answer

Calculation of Moment of Inertia of Rectangular Section

Moment of Inertia is the measure of a body's resistance to rotational motion. It is defined as the summation of the product of the mass of each particle of the object with the square of its perpendicular distance from the axis of rotation.

The moment of inertia of a rectangular section about its vertical centroidal axis is given by the formula:

I = bd^3/12

Where,

- b - width of the rectangular section
- d - depth of the rectangular section

Explanation of the Formula

The moment of inertia of a rectangular section can be calculated by dividing it into small elemental parts and then summing up those small parts.

- The rectangular section can be divided into small elemental parts of length dx and width b.
- The moment of inertia of each small elemental part about its centroidal axis is given by the formula: I = (1/12) * (dx*b^3)
- The distance of each small elemental part from the centroid of the rectangular section is (d/2).

Therefore, the moment of inertia of the rectangular section about its vertical centroidal axis can be calculated by integrating the moment of inertia of each small elemental part.

I = ∫ (d/2)^(-d/2) (1/12) * (dx*b^3) dx

I = (1/12) * b^3 * ∫ (d/2)^(-d/2) dx

I = bd^3/12

Hence, the moment of inertia of a rectangular section about its vertical centroidal axis is given by the formula I = bd^3/12

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