Question

Three hollow spheres of same mass and radius are placed as shown in figure. Find the $COM$ of the system.

• A. $(0,\frac{2}{3})$
• B. $(\frac{2}{3},0)$
• C. $(0,\frac{4}{3})$
• D. $(\frac{4}{3},0)$

Answer 1

The correct option is C $(0,\frac{4}{3})$


From the given figure, $R=1\text{unit}$ for all hollow spheres.
From symmetry, we can say $x_{COM}$ will be at the origin.
$y_{COM}=\frac{m_1{y}_1+m_2{y}_2+m_3{y}_3}{m_1+m_2+m_3}$
Here, mass of each sphere is same i.e $m_1=m_2=m_3=m$
$y_1$ for $COM$ of sphere $\left(1\right)$ from $\text{O}=0$
$y_2$ for $COM$ of sphere $\left(2\right)$ from $\text{O}=0$
$y_3$ for $COM$ of sphere $\left(3\right)$ from $\text{O}=4\text{units}$
$y_{COM}=\frac{m\left(0\right)+m\left(0\right)+m\left(4\right)}{m+m+m}=\frac{4}{3}\text{units}$
Hence, $COM$ of the system of spheres is at $(0,\frac{4}{3})$.