Question

Two thin discs each of mass M and radius r meter are attached to form a rigid body as shown in figure. The rotation inertia of this body about an axis perpendicular to the plane of disc B and 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 $5M{r}^2$

We have,

$AB=2r$

Now, about the given axis we have :

$I_B=\frac{M{r}^2}{2}$

$I_A=I_{com}+M(AB{)}^2$

$I_A=\frac{M{r}^2}{2}+M(2r{)}^2$

$I_A=\frac{9M{r}^2}{2}$

Hence, in total we have

$I_{total}=I_A+I_B$

$I_{total}=\frac{M{r}^2}{2}+\frac{9M{r}^2}{2}$

$I_{total}=5M{r}^2$