Question

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?

• A. $3M{R}^2$
• B. $\frac{2}{3}M{R}^2$
• C. $M{R}^2$
• D. $\frac{4}{5}M{R}^2$

Answer 1

The correct option is A $3M{R}^2$

$I=I_1+I_2+I_3=I_1+2I_2$

$I=\frac{M{R}^2}{2}+2(\frac{M{R}^2}{4}+M{R}^2)$

$I=\frac{M{R}^2}{2}+\frac{M{R}^2}{2}+2M{R}^2$

$I=3M{R}^2$.