A rectangular lamina of mass 2 kg is having side a=6 m and b=3 m. What is the moment of inertia of the rectangular lamina about an axis passing through the side 3 m as shown in figure below?
A
6 kg-m2
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B
15 kg-m2
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C
24 kg-m2
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D
14.8 kg-m2
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Solution
The correct option is C24 kg-m2 Let given lamina as lamina 1.
Assume another lamina identical to lamina 1 is attached to form a system as shown in figure.
Mass of system, M=(m+m) kg=2m kg We know, Moment of inertia of system about xx′;Inet=Ml212Inet=2m×(12)212=24m kg-m2=(24×2) kg-m2Inet=48 kg-m2..(i)
We know, Inet=I1+I2 As both lamina are identical and having same axis of rotation. ∴I1=I2⇒Inet=2I1⇒I1=Inet2I1=482 kg-m2=24 kg-m2
Alternate: MOI of the lamina about the given axis is given by I=ma23=2×623=24kg-m2