Find the center of mass $(x, y, z)$ of the following structure of four identical cubes if the length of each side of a cube is $1$ unit.

Three point particles of masses $1.0 \; kg$,$1.5 \; kg$,and $2.5 \; kg$ are placed at three corners of a right-angled triangle of sides $4.0 \; cm$,$3.0 \; cm$,and $5.0 \; cm$ as shown in the figure. The center of mass of the system is at a point:

The centre of mass of a thin rectangular plate (as shown in the figure) with sides of length $a$ and $b$,whose mass per unit area $(\sigma)$ varies as $\sigma = \frac{\sigma_0 x}{a b}$ (where $\sigma_0$ is a constant),would be . . . . . .

Two objects of masses $200 \ gm$ and $500 \ gm$ possess velocities $10 \hat{i} \ m/s$ and $3 \hat{i} + 5 \hat{j} \ m/s$ respectively. The velocity of their centre of mass in $m/s$ is

$A$ 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?

On what does the position of the center of mass of a rigid body depend?