Question

Four particles of masses $m,2m,3m$ and $4m$ respectively are placed on the periphery of a circle of radius $R$ as shown in figure then CM of the system contains the particle is at

• A. $(-\frac{R}{2},-\frac{R}{3})$
• B. $(-\frac{R}{6},-\frac{2R}{3})$
• C. $(-\frac{R}{5},-\frac{R}{5})$
• D. $(0,0)$

Answer 1

The correct option is C $(-\frac{R}{5},-\frac{R}{5})$

Given,

$m_1=m$

$m_2=2m$

$m_3=3m$

$m_4=4m$

Four particles are placed on the periphery of a circle of radius as shown in the figure of the given question.

center of mass of the system is

$CM=\frac{m_1{r}_1+m_2{r}_2+m_3{r}_3+m_4{r}_4}{m_1+m_2+m_3+m_4}$

Coordinate of center of mass in x-axis,

$X_{cm}=\frac{m\times R+2m\times 0+3m\times (-R)+4m\times 0}{m+2m+3m+4m}$

$X_{cm}=-\frac{R}{5}$

Coordinate of center of mass in y-axis is,

$Y_{cm}=\frac{m\times 0+2m\times R+3m\times 0+4m\times (-R)}{m+2m+3m+4m}$

$Y_{cm}=-\frac{R}{5}$

The coordinates of the center of mass of the system are

$CM=(-\frac{R}{5}.-\frac{R}{5})$

The correct option is C.