A section of a particular device looks as shown in the figure. It has two thin rods made up of a material of uniform linear mass density λ . The smaller rod is parallel to Y axis and in XOY plane whil

Question

A section of a particular device looks as shown in the figure. It has two thin rods made up of a material of uniform linear mass density $λ$ . The smaller rod is parallel to Y axis and in XOY plane while the larger rod is parallel to Z-axis in XOZ plane. Their dimensions are shown in the figure. The moment of inertia of the structure about Z axis shown is :

CT43 m6 diagram

TestHub · Accepted Answer

For the long rod parallel to z at x = 2 a , I z ​ = ( λ ⋅ 2 a ) ( 2 a ) 2 = 8 λ a 3 . For the small y -directed rod from x = 2 a , integrate x 2 d m along its length. Adding both rods gives I z ​ = 3 47 λ a 3 ​ .

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