Question

In the figure, the L-shaped shaded piece is cut from a metal plate of uniform thickness. The point that corresponds to the center of mass of the L-shaped piece is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B 2


Let the mass of a small square $=m$
Hence the mass of the square plate $=48m$
And the mass of the L shaped plate $=24m$

Let the position of centre of mass of L shaped structure be $\overrightarrow{r}$ and position of COM of the remaining structure be $\overrightarrow{r^{\prime }}$
Then,
$\overrightarrow{r^{\prime }}=\frac{48m\times 0-24m\times \overrightarrow{r}}{48m-24m}$
$\Rightarrow 24m\overrightarrow{r^{\prime }}=-24m\overrightarrow{r}$
$\Rightarrow \overrightarrow{r^{\prime }}=-\overrightarrow{r}$

Hence the position of C.M should be at '2'.