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Question

A disc of mass M and radius R is attached to a rectangular plate of the same mass M, breadth R and length 2R as shown in figure. The moment of inertia of the system about the axis AB passing through the centre of the disc and on the plane is I=1α(313MR2). Then, the value of α is


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Solution

IAB=Idisc+Iplate
Here,
IAB= Moment of inertia of the system about axis AB
Idisc= Moment of inertia of the disc about axis AB
Iplate= Moment of inertia of the plate about axis AB


Thus,
IAB=Idisc+(ICD+M(3R2)2)
(From Parallel Axis Theorem )
As we know,
MOI of disc about AB=Idisc=MR24
MOI of plate about CD=ICD=MR212
IAB=MR24+MR212+M(3R2)2
or IAB=3112MR2
So, α=4

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