Question

Four particles $A$, $B$, $C$ and $D$ having masses $m$, $2m$, $3m$ and $4m$ respectively are placed in order at the corners of a square of side $a$. Locate the centre of mass

• A. $\frac{a}{2}$ , $\frac{a}{2}$
• B. $\frac{a}{2}$, $\frac{7a}{10}$
• C. $\frac{a}{2}$,$\frac{3}{4}$
• D. None of these

Answer 1

The correct option is B

$\frac{a}{2}$, $\frac{7a}{10}$

Take the axes as shown in figure. The coordinates of the four particles are as follows:
$\begin{array}{cccc}Particle& mass& x-coordinate& y-coordinate\\ A& m& 0& 0\\ B& 2m& a& 0\\ C& 3m& a& a\\ D& 4m& 0& a\end{array}$
Hence, the coordinates of the centre of mass of the four-particle system are
$x=\frac{m.0+2ma+3ma+4m.0}{m+2m+3m+4m}=\frac{a}{2}$$y=\frac{m.0+2m.0+3ma+4ma}{m+2m+3m+4m}=\frac{7a}{10}$
The centre of mass is at $(\frac{a}{2},\frac{7a}{10})$.