Question

Two thin discs each of mass $M$ and radius $r$ are attached as shown to form a rigid body. The rotational 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

Answer: (D)

Moment of inertia of each disc about an axis through
the centre and perpendicular to the plane is $I_A=I_B=\frac{1}{2}M{r}^2$
Applying theorem of parallel axes, moment of inertia of disc $A$
about the given axis is $I_A^{\prime }=\frac{1}{2}M{r}^2+M(2r{)}^2=\frac{9}{2}M{r}^2$
$\therefore I=I_A^{\prime }+I_B=\frac{9}{2}M{r}^2+\frac{1}{2}M{r}^2=5M{r}^2$