$A$ uniform square plate is shown in the figure. Four identical squares are removed from its corners. If squares $1$ and $3$ are removed,where will the center of mass $(C.M.)$ be located?

Seven identical homogeneous bricks,each of length $L$,are arranged as shown in the figure. Each brick is displaced with respect to the one in contact by $\frac{L}{10}$. Calculate the $x$-coordinate of the centre of mass of this system relative to the origin $O$ as shown.

Choose the correct statement about the centre of mass $(CM)$ of a system of two particles.

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 ..........

$A$ 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?

Particles of masses $8 \, kg, 2 \, kg, 4 \, kg$,and $2 \, kg$ are placed at the vertices $A, B, C$,and $D$ of a square respectively. The distance of the center of mass of the system from vertex $A$ is $....... \, cm$. The length of the diagonal of the square is $80 \, cm$.