Question

Moment of inertia of a uniform circular disc about a diameter is $I$. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be

• A. $5I$
• B. $3I$
• C. $6I$
• D. $4I$

Answer 1

The correct option is C $6I$

$\text{Step 1: Apply perpendicular axis theorem}$ $\text{[}Ref.Fig.1]$

From perpendicular axis theorem

$I_x+I_y=I_z$

$I_1+I_2=I_3$

& $I_1=I_2=I$ (given)

$\Rightarrow I_3=2I$ $....\left(1\right)$

$\text{Step 2: Apply parallel axis theorem [Ref. Fig. 2]}$

$I^{\prime }=I_{COM}+m{a}^2$

(parallel Axis theorem)

Here $a=R$

So, $I_4=I_3+m{R}^2$

$=2I+m{R}^2$ $....\left(2\right)$

From eq. $\left(1\right)$ Moment of inertia of a disc about an axis passing through C.O.M. and perpendicular to its plane-

$I_3=\frac{m{R}^2}{2}=2I$

$\Rightarrow m{R}^2=4I$ $....\left(3\right)$

From $\left(1\right)$ & $\left(3\right)$

$I_4=2I+4I$

$I_4=6I$

Hence option C is correct