Question

Find the moment of inertia of uniform circular disc placed on the horizontal surface having origin as center. If the moment of inertia of disc along the axis passing through the the diameter is $2{\text{kg m}}^2$, find the moment of inertia of disc about the axis perpendicular to the plane of disc and passing through its centre.

• A. $2{\text{kg m}}^2$
• B. $4{\text{kg m}}^2$
• C. $6{\text{kg m}}^2$
• D. $8{\text{kg m}}^2$

Answer 1

The correct option is B $4{\text{kg m}}^2$

Given, $\text{MOI}$ about the axis passing through the diameter.

Moment of inertia about $x$-axis and $y$-axis is given by
$I_x=I_y=2{\text{kg m}}^2$
From the Perpendicular axis theorem,
$\text{MOI}$ of disc about the $z$-axis $\left(I_z\right)$ is given by
$I_z=I_x+I_y$
$\Rightarrow I_z=2+2$
$\Rightarrow I_z=4{\text{kg m}}^2$