Find the position of the center of mass of a system of two particles of masses $m_1$ and $m_2$ separated by a distance $L$.

The figure below shows a shampoo bottle in a perfect cylindrical shape. In a simple experiment,the stability of the bottle filled with different amounts of shampoo volume is observed. The bottle is tilted from one side and then released. Let the angle $\theta$ depict the critical angular displacement resulting in the bottle losing its stability and tipping over. Choose the graph that correctly depicts the fraction $f$ of shampoo filled ($f=1$ corresponds to completely filled) versus the tipping angle $\theta$.

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.

$A$ rod of length $L$ has non-uniform linear mass density given by $\rho(x)=a+b\left(\frac{x}{L}\right)^{2}$,where $a$ and $b$ are constants and $0 \leq x \leq L$. The value of $x$ for the centre of mass of the rod is at

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.

Obtain the position of the centre of mass of a thin rod of uniform density.