$A$ 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 $; m$)

Is the statement "$A$ particle has point volume" true or false?

Four identical spheres, each of radius $10 \,cm$ and equal mass $1 \,kg$, are placed on a horizontal surface touching each other such that their centers are located at the vertices of a square of side $20 \,cm$. What is the distance of their center of mass from the center of any sphere?

For a body,the center of volume is defined as $\frac{\int \vec{r} \, dV}{\int dV}$ over the complete body,where $dV$ is a small volume element of the body and $\vec{r}$ is the position vector of that small volume from the origin. Which of the following statements is correct?

Two objects $A$ and $B$ of masses $M$ and $m$ respectively,where $M > m$,are separated by a distance. They move towards each other under the influence of equal forces. At what point will they collide?

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 $1 \ \mathring A$: