Question

A uniform circular disc A of radius r is made from a copper plate of thickness t and another uniform circular disc B of radius 2r is made from a copper plate of thickness t/2. The relation between the moments of inertia, $I_A$ and $I_B$ is:

• A. $I_A>I_B$
• B. $I_A=I_B$
• C. $I_A<I_B$
• D. Depends on the values of t and r.

Answer 1

The correct option is C $I_A<I_B$

Let the density of the disc be $\rho$.

Disc A :

Mass of the disc $M_A=\rho \times [\pi r^2\times t]=\rho \pi r^{2}t$

Moment of inertia of disc A $I_A=\frac{1}{2}{M}_A(r{)}^2=\frac{\rho \pi r^{4}t}{2}$

Disc B :

Mass of the disc $M_B=\rho \times \left[\pi \right(2r{)}^2\times \frac{t}{2}]=2\rho \pi r^{2}t$

Moment of inertia of disc A $I_B=\frac{1}{2}{M}_B(2r{)}^2=2\rho \pi r^{4}t$

$⟹I_B>I_A$