Question

The moment of inertia of a uniform disc about the perpendicular axis through its centre of mass is $20{\text{kg m}}^2$. Then its moment of inertia about an axis along its diameter and in the plane of the disc will be

• A. $20{\text{kg m}}^2$
• B. $5{\text{kg m}}^2$
• C. $10{\text{kg m}}^2$
• D. $40{\text{kg m}}^2$

Answer 1

The correct option is C $10{\text{kg m}}^2$

Let $R=$ Radius of uniform disc
$M=$ mass of uniform disc
Given, $\text{MOI}$ about axis perpendicular to plane through centre
$I_z=\frac{M{R}^2}{2}=20{\text{kg m}}^2$​
Now, by perpendicular axis theorem and symmetry,
$I_x=I_y=\frac{I_z}{2}=10{\text{kg m}}^2$
Hence, moment of inertia about an axis along its diameter and in the plane of the disc will be $10{\text{kg m}}^2$