Question

A system of particles has its centre of mass at the origin. Then the x co-ordinates of the particle-
1. is positive for all particles
2. is negative for all particles
3. is positive for some particles and negative for some other particles
4. none of the above

Answer 1

Correct Answer - Option 3 : is positive for some particles and negative for some other particles

The correct answer is option 3) i.e. is positive for some particles and negative for some other particles

CONCEPT:

• Center of mass: Center of the mass of a body is the weighted average position of all the parts of the body with respect to mass.
  • The centre of mass is used in representing irregular objects as point masses for ease of calculation.
  • For simple-shaped objects, its centre of mass lies at the centroid.
  • For irregular shapes, the centre of mass is found by the vector addition of the weighted position vectors.
• The position coordinates for the centre of mass can be found by:
  \(C_x = \frac{m_1x_1 +m_2x_2 + ... m_nx_n}{m_1 + m_2 +... m_n}\)   \(C_y = \frac{m_1y_1 +m_2y_2 + ... m_ny_n}{m_1 + m_2 +... m_n}\)

EXPLANATION:

• The centre of mass is the algebraic sum of the products of mass of particles and their respective distances from a point of reference.
• The mass of a particle cannot take a negative value.
• Thus, the distances or coordinates of the particles should have negative and positive values for the centre of mass to be zero.