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The centre of mass of a system of particles lies at the origin. Which of the following statements is incorrect? (A) The number of particles to the right of the origin equals the number to the left. (B) The total mass to the right of the origin equals the total mass to the left. (C) The number of particles on the X-axis equals the number on the Y-axis. (D) If there is a particle on the positive X-axis, there must be at least one particle on the negative X-axis.
- (A) The number of particles to the right of the origin is equal to the number of particles to the left of the origin
- (B) The total mass of the particles to the right of the origin is same as the total mass to the left of the origin
- (C) The number of particles on X-axis should be equal to the number of particles on Y-axis
- (D) If there is a particle on the positive X-axis, there must be at least one particle on the negative X-axis.
Correct answer: (A) The number of particles to the right of the origin is equal to the number of particles to the left of the origin
Solution
The CM condition (sum of m*x = 0) constrains mass moments, not particle counts, so the claim that equal numbers of particles lie on each side is incorrect.
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