Question

Two bodies of masses $3\text{kg}$ and $2\text{kg}$ are located at $x=0\text{m}$ and $x=4\text{m}$ respectively. Find the position of the centre of mass of the system (with respect to mass $2\text{kg}$) .

• A. $\frac{8}{5}\text{m}$
• B. $2\text{m}$
• C. $\frac{12}{5}\text{m}$
• D. $3\text{m}$

Answer 1

The correct option is C $\frac{12}{5}\text{m}$


Let the position of COM be at $x=x\text{m}$
Taking the reference for measuring position at the origin ($x=0\text{m}$)

$x_1$ = distance of $m_1$ from origin
$x_2$ = distance of $m_2$ from origin

Applying formula for finding $x$-coordinate of COM:
$x_{\text{COM}}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}$
$=\frac{3\times 0+2\times 4}{3+2}=\frac{8}{5}$

Distance of COM from mass $m_1$ $=\frac{8}{5}\text{m}$
$\therefore$ Distance of COM from mass $m_2$ $=4-\frac{8}{5}=\frac{12}{5}\text{m}$