Question

Which of the following statements regarding ntre of mass is NOT true?

• A. For two particles of equal mass, the centre of mass lies exactly midway between them
• B. For three non-linear particles of equal mass, the centre of mass coincides with the centroid of the triangle formed by the particles
• C. When the total external force on a system is zero, the velocity of the centre of mass of the system remains constant
• D. For two particles of different masses, the centre of mass of the particles is nearer to the particle of lesser mass

Hint:

Tip: The centre of mass lies inversely proportional to mass; closer to the heavier object.

Answer 1

The Correct Option is D

Statement (4) is incorrect. The centre of mass lies **closer to the heavier mass**, not the lighter one. This is because the position of centre of mass in a two-particle system is given by: \[ x_{CM} = \frac{m_1x_1 + m_2x_2}{m_1 + m_2} \] and lies closer to the mass with greater magnitude. All other statements are standard facts about COM for symmetric systems and conservation of momentum.

Answer 2

Step 1: Understand the concept of center of mass (CM)
The center of mass of a system is the point where the total mass of the system can be considered to be concentrated.

Step 2: For two particles of masses \(m_1\) and \(m_2\) separated by a distance \(d\)
The position of the center of mass from the particle with mass \(m_1\) is given by:
\[ x = \frac{m_2 \times d}{m_1 + m_2} \]
This means the CM is closer to the particle with the larger mass because it is inversely proportional to the mass it is measured from.

Step 3: Analyze the given statement
The statement "For two particles of different masses, the centre of mass of the particles is nearer to the particle of lesser mass" is incorrect because the CM is always nearer to the particle with greater mass.

Step 4: Conclusion
Hence, the correct answer is:
"For two particles of different masses, the centre of mass of the particles is nearer to the particle of lesser mass" is NOT true.