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Moment of Inertia of a Disc

two circular ...

Question

two circular disks A & B of same mass and same thikness are made of 2 different metals whose densities are dA and dB(dA greater than dB).their moment of inertia about the axis passing throigh their cenre of gravity and perpendicular to their planes are IA and IB.which is greater IA or IB?

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Solution

$M o m e n t o f i n e r t i a o f a t h i n d i s k i s I = \frac{1}{2} M R^{2} n o w i f M_{A} = M_{B} t h e n A_{A} \times ρ_{A} = A_{B} \times ρ_{B} a s t h i c k e n s s i s s a m e f o r b o t h o f t h e m n o w i f ρ_{A} > ρ_{B} t h e n A_{B} > A_{A} s o R_{B} > R_{A} w h e r e R i s t e h r a d i u s . s o I_{B} > I_{A}$

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