Concepts Of Physics MCQ Edition [Volume 1]PhysicsCentre of Mass, Linear momentum, Collision
A system of particles has its centre of mass at the origin. It follows that
Options
- Athe quantity of particles to the right of the origin equals the quantity to the left
- Bif there is a particle with a positive x -coordinate, there must be at least one particle with a negative x -c
- Cthe aggregate mass of the particles to the right of the origin equals the aggregate mass to the left of the or
- Dthe number of particles on the X -axis must equal the number of particles on the Y -axis
Correct answer
B. if there is a particle with a positive x -coordinate, there must be at least one particle with a negative x -c
Step-by-step solution
The x -coordinate of the centre of mass of a system of particles is given by X_ cm = m_i x_i m_i Since the centre of mass is at the origin, X_ cm = 0 , which gives m_i x_i = 0 Since the mass m_i of each particle is always positive, if there is a particle with a positive x -coordinate ( x_i > 0 ), the term m_i x_i will be positive. For the sum m_i x_i to be zero, there must be at least one term with a negative value. This implies that there must be at least one particle with a negative x -coordinate. The number of p