Question

Two thin discs, each of mass $M$ and radius $r$ meter, are attached as shown in the fig. to form a rigid body. The rotational inertia of this body about an axis perpendicular to the plane of disc B passing through its centre is

• A. $2M{r}^2$
• B. $3M{r}^2$
• C. $4M{r}^2$
• D. $5M{r}^2$

Answer 1

The correct option is D $5M{r}^2$

The moment of inertia of the disc about the centroidal axis is $\frac{M{r}^2}{2}$.
The moment of inertia of the disc at A about the axis passing through B is given using parallel axis theorem as $\frac{M{r}^2}{2}+M(2R{)}^2$
Thus the total moment of inertia of the whole system is given as $\frac{M{r}^2}{2}+\frac{M{r}^2}{2}+M(2R{)}^2=5M{r}^2$