Question

# The mass density of the material of a T joint is 2 kg/m. The dimensions of this joint are shown in the figure. What is the approximate moment of inertia (MI) of the T joint about an axis passing through their common joining point and perpendicular to the plane of structure?

A
120 kg-m2
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B
240 kg-m2
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C
362 kg-m2
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D
426 kg.m2
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Solution

## The correct option is A 362 kg-m2The mass density of the material of the T joint, λ=2 kg/m Length of section AB: LAB=5 m Mass of section AB ∴mAB=λ×LAB=2×5=10 kg Similarly, LCD=8 m mCD=λ×LCD=2×8=16 kg ⇒ For section AB the axis YY′ is analogous to axis passing through mid point of a rod. ∴ MI of section AB about the axis, MIAB=mAB×L2AB12 ⇒MIAB=10×5212=10×2512=1256 kg-m2 ⇒ The axis YY′ is analogous to the axis passing through one end of a rod. ∴MICD=mCD×L2CD3=16×823 ⇒MICD=10243 kg-m2 Net MI of T joint is: MINet=MIAB+MICD ∴MINet=1256+10243≈362 kg-m2

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