Question

The center of mass of a uniform rod of mass m and length L will be at-
1. Middle point of the rod
2. L/3 from one end of the rod
3. L/4 from one end of the rod
4. L/12 from one end of the rod

Answer 1

Correct Answer - Option 1 : Middle point of the rod

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:

• Since a uniform rod is a symmetrical body that has no variation in its mass distribution throughout the body. So the center of mass will be at the middle point of the rod. Hence option 1 is correct.