Question

Two objects $A$ and $B$ of weight 10 kg and 20 kg respectively are kept at two points on the $x$-axis. B is moved 9 cm along the $x$-axis. By what distance A should be moved to keep the centre of mass the same?

• A. 21 cm
• B. 18 cm
• C. 15 cm
• D. 12 cm

Answer 1

Answer: (B)

To keep centre of mass at same point
$r_{CM}\left(before\right)=r_{CM}\left(Final\right)$
$\frac{m_1{r}_1+m_2{r}_2}{m_1+m_2}=\frac{m_1\left(r_1+x\right)+m_2\left(r_2+9\right)}{m_1+m_2}$
$m_1{r}_1+m_2{r}_2=m_1{r}_1+m_1{x}_1+m_2{r}_2+9m_2{m}_{1}x=-9m_2$
$x=\frac{9m_2}{m_1}$ [neglecting negative sign]
$x=9\times \frac{20}{10}=18cm$