Question

$n$ particles of the same mass are placed on the $x$ - axis. If the particles are placed at $x=1,2,3,..........n$ respectively, then find the location of COM.

• A. $\frac{(n+1)}{2}$
• B. $\frac{n(n+1)}{2}$
• C. $\frac{n(n-1)}{2}$
• D. None of the above

Answer 1

The correct option is A $\frac{(n+1)}{2}$

We know,
$X_{com}=\frac{m_1{x}_1+m_2{x}_2+m_3{x}_3+-----+m_n{x}_n}{m_1+m_2+m_3+-----m_n}$

$\Rightarrow X_{com}=\frac{m.1+m.2+m.3+-------m.n}{m+m+------m}$

$=\frac{m[1+2+3-----n]}{nm}=\frac{n(n+1)}{2n}=\frac{(n+1)}{2}$