Two circular discs are of same thickness. The diameter of A is twice that of B. The moment of inertia of A as compared to that of B is

Question

Two circular discs are of same thickness. The diameter of A is twice that of B. The moment of inertia of A as compared to that of B is (A) twice as large (B) four times as large (C) eight times as large (D) 16 times as large

Tardigrade Admin · Accepted Answer

Mass of disc propto area, MA=4 MB (as RA=2 RB ) (IA/IB)=((1/2) MA RA2/(1)2 MB RB2)=(4 MB ×(2 RB)2/MB × RB2)=16

Q. Two circular discs are of same thickness. The diameter of $A$ is twice that of $B$ . The moment of inertia of $A$ as compared to that of $B$ is

twice as large

four times as large

eight times as large

16 times as large

Mass of disc $\propto$ area, $M_{A} = 4 M_{B}$ (as $R_{A} = 2 R_{B}$ )
$\frac{I _{A}}{I _{B}} = \frac{\frac{1}{2} M _{A} R _{A}^{2}}{\frac{1}{2} M _{B} R _{B}^{2}} = \frac{4 M _{B} \times ( 2 R _{B} ) ^{2}}{M _{B} \times R _{B}^{2}} = 16$

Q. Two circular discs are of same thickness. The diameter of A is twice that of B. The moment of inertia of A as compared to that of B is