Two point masses of $1.5 \ g$ and $2.5 \ g$ are placed at a distance of $16 \ cm$ from each other. If the center of mass is at a distance $x$ from the $1.5 \ g$ mass,then $x = \dots \ cm$.

Find the centre of mass of a triangular lamina.

Three rods of equal mass are arranged as shown in the figure. Find the coordinates of the center of mass of the system.

$A$ 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?

$A$ uniform rod of mass $400 \ g$ and length $1 \ m$ is pivoted at one end. It is displaced by an angle of $60^o$. The increase in its potential energy is ....... $J$.

The distance between the carbon atom and the oxygen atom in a carbon monoxide molecule is $1.1 Å$. Given,mass of carbon atom is $12 amu$ and mass of oxygen atom is $16 amu$. Calculate the position of the centre of mass of the carbon monoxide molecule.