Question

Let $I_A$ and $I_B$ be the moments of inertia of two solid cylinders $A\&B$ of identical dimensions and size, about their axis of symmetry. Solid cylinders $A\&B$ are made of aluminium and iron respectively, then the relation between $I_A$ and $I_B$ is

• A. $I_A<I_B$
• B. $I_A=I_B$
• C. $I_A>I_B$
• D. Relation between $I_A$ and $I_B$ cannot be predicted as it depends on the frame of reference.

Answer 1

The correct option is A $I_A<I_B$

Moment of inertia $\left(\text{MOI}\right)$ depends on the geometrical shape and mass distribution of the body about the axis of rotation.

Geometrical shape and dimensions are identical for both the solid cylinders. However, solid cylinder $B$ being made of iron has a higher density compared to solid cylinder $A$ made of aluminium.
$\therefore$ Mass distribution is higher for cylinder $B$ about axis of rotation.
$\Rightarrow I_A<I_B$