This question examines the concept of center of mass location.
Design multiple-choice questions (MCQs) for CBSE Class 11 Physics, Chapter 6: “System of Particles and Rotational Motion,” based on the NCERT syllabus for 2024-2025. Cover essential topics like center of mass, torque, angular momentum and rotational dynamics. Include a mix of theoretical and numerical questions with varying difficulty levels to assess students’ understanding and problem-solving skills. Ensure clarity, precision and alignment with NCERT guidelines to help students prepare efficiently and deepen their knowledge of rotational motion.
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The center of mass of a two-particle system lies closer to the particle with the greater mass. This is because the position of the center of mass (COM) is calculated as a weighted average of the positions of the two particles, with their respective masses serving as the weights.
Mathematically, the center of mass for a two-particle system can be expressed as:
\[ x_{COM} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2} \]
Here:
– \( m_1 \) and \( m_2 \) are the masses of the two particles.
– \( x_1 \) and \( x_2 \) are the positions of the two particles along a straight line.
From this formula, it is clear that:
– If \( m_1 > m_2 \), the center of mass will be closer to \( x_1 \).
– If \( m_2 > m_1 \), the center of mass will be closer to \( x_2 \).
This principle holds true regardless of the spatial dimension, with similar calculations extending to three-dimensional systems using the vector positions of the particles.
This question related to Chapter 6 physics Class 11th NCERT. From the Chapter 6. System of particle and Rotational Motion. Give answer according to your understanding.
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