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The center of mass of a uniform rod lies
1. At its's end
2. At it's middle point
3. At it's center of cross sectional area
4. Depends upon material

1 Answer

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Correct Answer - Option 2 : At it's middle point

CONCEPT:

  • Center of mass (R ): The centre 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 centre 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.
  • The centre of mass of the body is given as,

\(⇒ X=\frac{x_1m_1+x_2m_2+...+x_nm_n}{m_1+m_2+...+m_n}\)

\(⇒ Y=\frac{y_1m_1+y_2m_2+...+y_nm_n}{m_1+m_2+...+m_n}\)

\(⇒ Z=\frac{z_1m_1+z_2m_2+...+z_nm_n}{m_1+m_2+...+m_n}\)

Where X = centre of mass on x-axis, Y = centre of mass on y-axis, Z = centre of mass on z-axis, and m1, m2,...,mn = mass of the n particles

EXPLAINATION:

  • From the above discussion, it is clear that the center of mass lies where the whole mass of the body can be concentrated.
  • Therefore for a uniform rod, the whole mass can be assumed to be concentrated at its middle point.
  • Hence, option (2) is correct

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