$A$ square plate and a circular disc of uniform density are arranged as shown in the figure. The center of mass of this combined system will be .........

The velocities of three particles of masses $20 \ g$,$30 \ g$ and $50 \ g$ are $10 \hat{i}$,$10 \hat{j}$ and $10 \hat{k}$,respectively. The velocity of the centre of mass of the three particles is

Center of mass of a system of three particles of masses $1 \, kg, 2 \, kg, 3 \, kg$ is at the point $(1 \, m, 2 \, m, 3 \, m)$ and center of mass of another group of two particles of masses $2 \, kg$ and $3 \, kg$ is at point $(-1 \, m, 3 \, m, -2 \, m)$. Where should a $5 \, kg$ particle be placed so that the center of mass of the system of all these six particles shifts to the center of mass of the first system?

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 $1 \ \mathring A$:

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

The linear mass density $(\lambda)$ of a rod of length $L$ kept along the $x$-axis varies as $\lambda = \alpha + \beta x$,where $\alpha$ and $\beta$ are positive constants. The centre of mass of the rod is at ..........