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

Match Column-$I$ with Column-$II$.

Column-$I$	Column-$II$
$(1)$ $\frac{{{m_1}{m_2}}}{{{m_1} + {m_2}}}$	$(a)$ Reduced mass of a two-particle system
$(2)$ $\frac{{{r_1} + {r_2}}}{2}$	$(b)$ Position vector of the center of mass for a system of two equal masses

The centre of mass of a triangle shown in the figure has coordinates

Three equal masses are placed at $(0,0)$,$(a,0)$,and $\left( \frac{a}{2}, \frac{a\sqrt{3}}{2} \right)$. Find the coordinates of the center of mass.

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

Mass is distributed uniformly over a thin square plate. If two end points of a diagonal are $(-2, 0)$ and $(2, 2)$,what are the coordinates of the centre of mass of the plate?