Two particles of masses $2$ g and $4$ g are situated at the opposite ends, $A$ and $B$ of a wooden bar respectively. Let $l(AB) = 9$ cm. The center of mass of the system will be

Four particles of masses $1\,kg, 2 \,kg, 3 \,kg$ and $4\, kg$ are placed at the four vertices $A, B, C$ and $D$ of a square of side $1\, m$ as shown in the figure. The coordinates of the centre of mass of the particles are:

Two particles of masses $200 \ g$ and $500 \ g$ are moving with velocities $10 \ \hat{i} \ m/s$ and $3 \ \hat{i} + 5 \ \hat{j} \ m/s$ respectively. The velocity of the center of mass of the system is:

Three particles of masses $20 \, g$,$30 \, g$,and $50 \, g$ have velocities $10 \, \hat{i}$,$10 \, \hat{j}$,and $10 \, \hat{k}$ respectively. The velocity of the center of mass of these three particles is:

$A$ 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 .........

$A$ thin rod of length $L$ is placed along the $X$-axis such that one of its ends is at $x = 0$ and the other is at $x = L$. Its linear mass density (mass/length) varies with $x$ as $k(x/L)^n$,where $n$ is any positive number or zero. If the graph of the center of mass $x_{cm}$ versus $n$ is plotted for the rod,which of the following graphs is correct?