Center of Mass and Mass Moments – Rankers Physics

Calculation of Center of Mass: Practice Problem & Solution

Assertion (A): The centre of mass of a system of two particles is closer to the heavier particle. Reason (R): Algebraic sum of mass moments about centre of mass is zero.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

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:

For a two-particle system, the center of mass \( R_{CM} \) is defined such that the sum of mass moments about it is zero: \( m_1r_1 = m_2r_2 \). If \( m_1 > m_2 \), then \( r_1 < r_2 \), meaning the COM is closer to the heavier particle.

Thus both A and R are true, and R explains A.

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