A circular disc $$D_1$$ of mass M and radius R has two identical discs $$D_2$$ and $$D_3$$ of the same mass M and radius R attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axis OO', passing through the centre of $$D_1$$, as shown in the figure, will be

Moment of inertia of central disc $$D_1$$ about axis $$OO'$$: $$I_1 = \frac{1}{2}MR^2$$

Moment of inertia of outer disc $$D_2$$ (or $$D_3$$) about its own diameter parallel to $$OO'$$: $$I_{\text{cm}} = \frac{1}{4}MR^2$$

Distance from center of $$D_1$$ to center of $$D_2$$ (or $$D_3$$): $$d = R$$

Applying parallel axis theorem for one outer disc ($$D_2$$ or $$D_3$$) about axis $$OO'$$:

$$I_2 = I_3 = I_{\text{cm}} + Md^2 = \frac{1}{4}MR^2 + MR^2 = \frac{5}{4}MR^2$$

Total moment of inertia of the system:

$$I_{\text{total}} = I_1 + I_2 + I_3 = \frac{1}{2}MR^2 + 2\left(\frac{5}{4}MR^2\right) = \frac{1}{2}MR^2 + \frac{5}{2}MR^2 = 3MR^2$$