Two atoms of oxygen are located at $r_1$ and $r_2$. Their centre of mass is at

The linear mass density of a rod of length $L$ varies as $\lambda = kx^2$,where $k$ is a constant and $x$ is the distance from one end. The position of the centre of mass of the rod is:

For a system consisting of two objects,when can they be treated as point particles?

$(a)$ Centre of gravity $(C.G.)$ of a body is the point at which the weight of the body acts.
$(b)$ Centre of mass coincides with the centre of gravity if the earth is assumed to have an infinitely large radius.
$(c)$ To evaluate the gravitational field intensity due to any body at an external point,the entire mass of the body can be considered to be concentrated at its $C.G.$
$(d)$ The radius of gyration of any body rotating about an axis is the length of the perpendicular dropped from the $C.G.$ of the body to the axis of rotation.
Which one of the following pairs of statements is correct?

The position of the centre of mass of a cube of uniform density will be at

In the $HCl$ molecule,the separation between the nuclei of the two atoms is about $1.27 \, \mathring{A}$ $(1 \, \mathring{A} = 10^{-10} \, m)$. The approximate location of the centre of mass of the molecule from the hydrogen atom,assuming the chlorine atom to be about $35.5$ times as massive as the hydrogen atom,is ....... $\mathring{A}$.