Locate the centre of mass of the arrangement shown in the figure. The three rods are identical in mass and length.

$A$ $T$-shaped object with dimensions shown in the figure is lying on a smooth floor. $A$ force $\vec{F}$ is applied at point $P$ parallel to $AB$,such that the object has only translational motion without rotation. Find the location of $P$ with respect to $C$.

$A$ uniform rod of length $L$ is placed along the $x$-axis with one end at the origin. If the linear mass density of the rod varies as $\lambda(x) = ax$,where $a$ is a constant,find the position of the centre of mass of the rod.

The distance between the two atoms in an $HCl$ molecule is approximately $1.27 \mathring{A}$ $(1 \mathring{A} = 10^{-10} \text{ m})$. The chlorine atom is $35.5$ times heavier than the hydrogen atom. The position of the center of mass from the hydrogen atom is approximately ..... $\mathring{A}$.

Two objects of masses $200 \text{ g}$ and $500 \text{ g}$ possess velocities $10 \hat{i} \text{ m/s}$ and $(3 \hat{i} + 5 \hat{j}) \text{ m/s}$ respectively. The velocity of their centre of mass in $\text{m/s}$ is:

Seven identical homogeneous bricks,each of length $L$,are arranged as shown in the figure. Each brick is displaced with respect to the one in contact by $\frac{L}{10}$. Calculate the $x$-coordinate of the centre of mass of this system relative to the origin $O$ as shown.