Question

A circular disc $A$ of radius $r$ is made from an iron plate of thickness $t$ and another circular disc $B$ of radius $4 r$ and thickness $t / 4$. The relation between moments of inertia $I_{A}$ and $I_{B}$ about the same axis is:

• A. $I_{A} > I_{B}$
• B. $I_{A} = I_{B}$
• C. $I_{A} < I_{B}$
• D. depends on the actual values of $t$ and $r$

Answer 1

Answer: (C)

$m_{A}=$ volume $\times$ density $=\pi x^{2} t \rho$
$I_{A}=\frac{1}{2} m_{A} r^{2}=\frac{1}{2} \pi r^{4} \rho t$
Similarly $I_{B}=\frac{1}{2} \pi(4 r)^{4} \rho\left(\frac{t}{4}\right)=64 I_{A}$
Clearly $I_{B}>I_{A}$