# The centre of mass of a system of particles is at the origin. This means that-

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The centre of mass of a system of particles is at the origin. This means that-
1. the number of particles on the right and left side of the origin is the same
2. the total mass of particles on the right side of the origin equals the total mass of particles on the left side of the origin
3. the number of particles on the x-axis and y-axis should be the same
4. none of the above

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Correct Answer - Option 4 : none of the above

The correct answer is option 4) i.e. none of the above

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 center of mass is used in representing irregular objects as point masses for ease of calculation.
• For simple-shaped objects, its center of mass lies at the centroid.
• For irregular shapes, the center of mass is found by the vector addition of the weighted position vectors.
• The position coordinates for the center 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:

• For the centre of mass to be at the origin, the sum of the product of the mass and respective distances from the origin must equal to zero.
• That means the centre of mass depends on the mass and distance simultaneously.
• The first three options only indicate a relationship with the number of particles and mass separately.
• Hence, none of the above options relates to the given statement.