Define ‘Moment of inertia’ and write mathematical expression of square and quarter circle with both axis.

Define ‘Moment of inertia’ and write mathematical expression of square and quarter circle with both axis.
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Answer :

Moment of inertia of a body about any axis is equal to the product of the area of the body and square of the distance of its centroid from that axis. 

OR 

Moment of inertia of a body about any axis is defined as the sum of second moment of all elementary areas about that axis.

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The moment of inertia of a semi-circle of radius r with respect to a centroidal axis parallel to the diameter is a.0.33 r2 b.0.11 r2 c.0.055 r2 d.0.05 r2 e.0.22 r2

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Polar moment of inertia is a.Applicable to masses whereas moment of inertia is applicable to area only b.The moment of inertia for an area ralative to a line or axis which is out the plane of area c.Same as moment of inertia d.The moment of inertia for an area relative to a line or axis parallel to the centroidal axis e.The moment of inertia for an area relative to a line or axis perpendicular to the plane of the area

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The moment of inertia of a hollow circular section whose external diameter is 8 cm and interial diameter is 6 cm about the axis passing through its centre is a.66.8 cm4 b.137.5 cm4 c.550 cm4 d.33.4 cm4 e.275 cm4

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If M, I, R, E, F, and Y are the bending moment, moment of inertia, radius of curvature, modulus of elasticity stress and the depth of the neutral axis at section, then (A) M/I = R/E = F/Y (B) I/M = R/E = F/Y (C) M/I = E/R = E/Y (D) M/I = E/R = Y/F

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At any point of a beam, the section modulus may be obtained by dividing the moment of inertia of the section by (A) Depth of the section (B) Depth of the neutral axis (C) Maximum tensile stress at the section (D) Maximum compressive stress at the section

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