Explanation

(c) For translator motion the force should be applied on the centre of 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 rod $CD$ will be 2$m$.
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 $ie$, mass $m$ is placed at $y_{1}$ and mass $2m$ is placed at $y_{2}$.
Taking point $c$ at the origin position vector of points $y_{1}\ and\ y_{2}$ can be written as
$\mathbf{r}_{1} = 2l\mathbf{j},\ \mathbf{r}_{2} = l\mathbf{j}$
and $m_{1} = m\ and\ m_{2} = 2m$
Position vector of centre of mass of the system
$r_{CM} = \frac{m_{1}r_{1} + m_{2}r_{2}}{m + m_{2}} = \frac{m2l\widehat{j} + 2ml\widehat{j}}{m + 2m} = \frac{4ml\widehat{j}}{3m} = \frac{4l\widehat{j}}{3}$