An isolated particle of mass $m$ is moving in a horizontal $x-y$ plane along the $x-$axis at a certain height above the ground. It suddenly explodes into two fragments of masses $m/4$ and $3m/4$. An instant later,the smaller fragment is at $y = 15 \ cm$. The larger fragment at this instant is at $y = \dots \ cm$.

In the $HCl$ molecule,the separation between the nuclei of the two atoms is about $1.27 \; \mathring{A} \; (1 \; \mathring{A} = 10^{-10} \; m)$. Find the approximate location of the center of mass $(CM)$ of the molecule,given that a chlorine atom is about $35.5$ times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus.

Two bodies of mass $1 \ kg$ and $3 \ kg$ have position vectors $\hat{i} + 2\hat{j} + \hat{k}$ and $-3\hat{i} - 2\hat{j} + \hat{k}$,respectively. The centre of mass of this system has a position vector:

Two particles of masses $M$ and $4M$ are released from a distance of $10 \ m$ from each other. Find the point of collision from the smaller particle in $meters$.

The distance of the centre of mass of a solid uniform cone from its vertex is $z_0$. If the radius of its base is $R$ and its height is $h$,then $z_0$ is equal to:

Two particles of masses $5 \,g$ and $3 \,g$ are separated by a distance of $40 \,cm$. The centre of mass of the system of these two particles