Question

Two blocks of masses 10 kg and 20 kg are placed on the X-axis.The first mass is moved on the axis by a distance of 2 cm.By what distance should the second mass be moved to keep the position of the centre of mass unchanged?

Answer 1

Two masses $m_1$ and $m_2$ are placed on the X-axis.

$m_1=10kg,m_2=20kg$

The first mass is displaced by distance of 2 cm.

$\therefore X_{cm}=\frac{m_a{x}_1+m_2{x}_2}{m_1+m_2}$

$=\frac{10\times 2+20x_2}{30}$

$\Rightarrow 0=\frac{20+20x_2}{30}$

$\Rightarrow 20+20x_2=0\Rightarrow 20=-20x_2$

$\Rightarrow x_2=-1$

$\therefore$ Second mass should be displaced by a distance 1 cm towards left so as to keep the position of centre of mass unchanged.