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