Question

Two discs of radii $5\text{m}$ and $3\text{m}$ are joined together along their circumference as shown in the figure below. Find the centre of mass of the system of two discs

• A. $(6,0)\text{m}$
• B. $(5,0)\text{m}$
• C. $(7,0)\text{m}$
• D. $(4,0)\text{m}$

Answer 1

The correct option is C $(7,0)\text{m}$

Given, $m_1=3\text{kg}$ and $m_2=1\text{kg}$


Coordinates of $COM$ of disc $1$, $(x_1,y_1)=(5,0)\text{m}$
Coordinates of $COM$ of disc $2$, $(x_2,y_2)=(13,0)\text{m}$

$x$- coordinate of COM of the system is given by
$x_{com}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}$
$=\frac{3\times 5+1\times 13}{3+1}=\frac{28}{4}\text{m}=7\text{m}$
$x_{com}=7\text{m}$

Both discs are symmetric about $x$ - axis. So, $y$ coordinate of $COM$ of the system is zero
So, centre of mass of the system of two discs is at $(7,0)\text{m}$