Three point masses $1 \mathrm{~kg}, 2 \mathrm{~kg}$ and 3 kg are placed as in the figure on x -axis

Question

Three point masses $1 \mathrm{~kg}, 2 \mathrm{~kg}$ and 3 kg are placed as in the figure on x -axis Distance of centre of mass from 1 kg is

Professor PC Thomas Classes · Answer

Let $1 \mathrm{kg}$ be at origin (0). Distance of COM $x_{com} = \frac{m_1 x_1 + m_2 x_2 + m_3 x_3}{m_1 + m_2 + m_3}$. Without the figure, based on common questions, if they are placed at $x=0, 1, 2$ respectively, $x_{com} = \frac{1(0) + 2(1) + 3(2)}{1+2+3} = \frac{8}{6} = \frac{4}{3} \mathrm{m}$. Or if at $x=1,2,3$ distance from $1\mathrm{kg}$ could be something. (We'll provide a generic formula explanation).