Question

Two circular discs $A$ and $B$ of equal masses and thicknesses but are made of metals with densities $d_{A}$ and $d_{B}\left(d_{ A }>d_{ B }\right)$. If their moments of inertia about an axis passing through the centre and normal to the circular faces be $I_{A}$ and $I_{B}$, then

• A. $I_{A} = I_{B}$
• B. $I_{A} > I_{B}$
• C. $I_{A} < I_{B}$
• D. $I_{A} \geq I_{B}$

Answer 1

Answer: (C)

mass = volume $\times$ density
$ \Rightarrow M=\left(\pi R^{2} t\right) d \ldots$ (1)
where $t$ is thickness
$I=\frac{M R^{2}}{2}\ldots$ (2)
From (1) and (2), we get:
$I=\frac{M^{2}}{2 \pi d t} \Rightarrow I \propto \frac{1}{d} \Rightarrow I_{A} < I_{B}$