64. What is the formula of theorem of perpendicular axis ?
(A) Izz = Ixx - TYY
(C) Izz - Ixx = lyy
(D) None of these
(B) Iz = Ixx + Ak
Answers
Answer:
B) I Z =I X + I Y
Explanation:
where, I X and I Y are the moments of inertia of plane lamina about the perpendicular axes X and Y, respectively which lie in the plane of lamina and intersect each other.
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Answer: The correct formula is (B) Izz = Ixx + Iyy.
Step-by-step explanation:
This formula is known as the "Theorem of Perpendicular Axes".
The theorem states that for any plane section perpendicular to one of the coordinate axes, the sum of the moments of inertia of the section about the two perpendicular axes is equal to the moment of inertia of the section about the axis perpendicular to the plane. In other words, if we consider the x-axis and y-axis to be perpendicular to each other, then the moment of inertia of the section about the z-axis (Izz) is equal to the sum of the moments of inertia of the section about the x-axis (Ixx) and the y-axis (Iyy).
The theorem of perpendicular axes is a fundamental concept in the study of mechanics and is used in the analysis of beam bending, torsion, and other mechanical systems. It is important to note that the theorem is only applicable to sections perpendicular to one of the coordinate axes and does not apply to sections that are not perpendicular to the coordinate axes.
In summary, the formula Izz = Ixx + Iyy is a useful tool for determining the moment of inertia of a cross-sectional area about different axes. This information can be used to design and analyze various mechanical systems, such as beams and shafts, to determine their strength and stability.
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