Question

A semicircular plate of mass $m$ has radius $r$ and centre $c$. The centre of mass of the plate is at a distance $x$ from its centre $c$. Its moment of inertia about an axis passing through its centre of mass and perpendicular to its plane is

• A. $\frac{m{r}^2}{2}$
• B. $\frac{m{r}^2}{4}$
• C. $\frac{m{r}^2}{2}+m{x}^2$
• D. $\frac{m{r}^2}{2}-m{x}^2$

Answer 1

Answer: (D)

Given,
mass of a semicircular plate $=m$
radius of semicircular plate $=r$
According to the question we can drawn the following diagram,

Now, from the parallel axis theorem,
$I_c=I_{cm}+m{x}^2$
$I_{cm}=I_c-m{x}^2$
$I_c=\frac{m{r}^2}{2}$
Hence, moment of inertia of semicircular plate about an axis passing through its centre of mass and perpendicular to it's plane is
$I_{cm}=\frac{m{r}^2}{2}-m{x}^2$