$A$ rod of length $3 \; m$ has a linear mass density that is directly proportional to the distance $x$ from one of its ends. Find the position of its centre of gravity from that end. (in $; m$)

Which of the following statements regarding the centre of mass is $NOT$ true?

The moment of inertia of an $HCl$ molecule about an axis passing through its centre of mass and perpendicular to the line joining the $H^+$ and $Cl^-$ ions is,if the interatomic distance is $1 \ \mathring A$:

If two bodies of masses $2 \,kg$ and $3 \,kg$ are moving at right angles with velocities $20 \,m \,s^{-1}$ and $10 \,m \,s^{-1}$ respectively, then the velocity of the centre of mass of the system of the two bodies is

In an $HCl$ molecule,the distance between the nuclei of the two atoms is $1.27 \ \mathring A$. The $Cl$ atom is approximately $35.5$ times heavier than the $H$ atom. The center of mass of this molecule will be at a distance of approximately ....... $\mathring A$ from the center of the $H$ atom.

The centre of mass of a system of particles does not depend on