Centre of Mass Questions

A body A of mass $M$ while falling vertically downwards under gravity breaks into two parts; a body B of mass $1/3M$ and a body C of mass $2/3M$. The centre of mass of bodies B and C taken together shifts compared to that of body A towards:

A ‘T’ shaped object with dimensions shown in the figure, is lying on a smooth floor. A force $F$ is applied at the point $P$ parallel to $AB$, such that the object has only the translational motion without rotation. Find the location of $P$ with respect to $C$:

A thin rod of length $L$ is lying along the $x$ -axis from $x=0$ to $x=L$. Its linear density $\lambda$ varies as $\lambda =k(x/L{)}^n$. Which graph best approximates the dependence of the position $x_{CM}$ of the centre of mass on $n$ ($n\ge 0$)?