Explanation

(a) For translatory motion the force should be applied on the centre of the mass of the body. So we have to calculate the location of centre of mass of ‘$T$’ shaped object.
Let mass of rod $AB$ is $m$ so the mass of the rod $CD$ will be $2m$
Let $y_{1}$ is the centre of mass of rod $AB$ and $y_{2}$ is the centre of mass of rod $CD$. We can consider that whole mass of the rod is placed at their respective centre of mass $i.e.,$ mass $m$ is placed at $y_{1}$ and mass $2m$ is placed at $y_{2}$
Taking point ‘$C$’ at the origin position vector of point $y_{1}$ and $y_{2}$ can be written as $\overrightarrow{r_{1}} = 2l\ \widehat{j},\ \overrightarrow{r_{2}} = l\widehat{j}$ and $m_{1} = m$ and $m_{2} = 2m$
Position vector of centre of mass of the system
${\overrightarrow{r}}_{cm} = \frac{m_{1}{\overrightarrow{r}}_{1} + m_{2}\overrightarrow{r_{2}}}{m_{1} + m_{2}} = \frac{m2l\widehat{j} + 2ml\widehat{j}}{m + 2m} = \frac{4ml\widehat{j}}{3m} = \frac{4}{3}l\widehat{j}$
Hence the distance of centre of mass from $C = \frac{4}{3}\ l$