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Find the centre of mass of three masses 1 kg, 4 kg and 8 kg which are placed at (2, 1), (-1, 2) and (0, 4) respectively.
1. (1, 2)
2. (-0.2, 3.2)
3. (0.6, 2.4)
4. (-1.2, 2.4)

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Best answer
Correct Answer - Option 2 : (-0.2, 3.2)

CONCEPT:

  • Center of mass (RCM): The center of mass of the body is a point where the whole mass of the body may be assumed to be concentrated for describing its translatory motion.
    • The center of mass of a system of particles is that single point that moves in the same way in which a single particle having the total mass of the system and acted upon by the same external force would move.
  • Mathematically center of mass for n – particle is written as

\({\vec R_{CM}} = \frac{{{m_1}{{\vec r}_1} + {m_2}{{\vec r}_2} + {m_3}{{\vec r}_3} - - - - - - - {m_n}{{\vec r}_n}}}{{{m_1} + {m_2} + {m_3} - - - - - - - {m_n}}}\)
EXPLANATION
:

Given -  m1 = 1 kg, m2 = 4 kg and m1 = 8 kg

  • The Centre of mass in direction of the x−axis is 

\(\Rightarrow x_{cm}=\frac{1\times 2+4\times (-1)+8\times 0}{13}=-0.153 \approx-0.2\)

  • The Centre of mass in direction of the y−axis is 

\(\Rightarrow y_{cm}=\frac{1\times 1+4\times 2+8\times 4}{13}=\frac{41}{13}=3.15\approx3.2\)

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