Center of Mass of Two Particles – Rankers Physics

Calculation of Center of Mass: Practice Problem & Solution

Two particles of masses \(2\text{ kg}\) and \(6\text{ kg}\) located at the point \((1\text{ m}, 1\text{ m}, 1\text{ m})\) and \((2\text{ m}, 2\text{ m}, 1\text{ m})\) respectively. The distance of centre of mass from \(2\text{ kg}\) mass will be
\(\frac{\sqrt{2}}{4}\text{ m}\)
\(\frac{3\sqrt{2}}{4}\text{ m}\)
\(\frac{1}{\sqrt{2}}\text{ m}\)
\(\frac{3\sqrt{2}}{8}\text{ m}\)

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Calculation of Center of Mass. Understanding the underlying formula is key to arriving at the correct answer below:

Distance between masses is \(d = \sqrt{(2-1)^2+(2-1)^2+0^2} = \sqrt{2}\text{ m}\)
Distance of center of mass from \(m_1\) is \(r_1 = \frac{m_2 d}{m_1+m_2} = \frac{6\sqrt{2}}{8} = \frac{3\sqrt{2}}{4}\text{ m}\).

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