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Identify the INCORRECT statement regarding a system of particles analyzed in the centre of mass (CM) frame.

1. The total linear momentum of the system in the CM frame is zero.
2. The kinetic energy of the system in the CM frame is the minimum possible kinetic energy of the system in any inertial frame.
3. If a non-zero impulsive external force acts on the system, the linear momentum of the system cannot be conserved.
4. If a non-zero external force acts on the system, it may not be possible to conserve the mechanical energy of the system.

Correct answer: If a non-zero impulsive external force acts on the system, the linear momentum of the system cannot be conserved.

Solution

Option A is correct: in the CM frame the total momentum is zero by definition. Option B is correct: KE_lab = KE_cm + (1/2)*M*v_cm², so KE in the CM frame is minimum over all inertial frames. Option D is correct: a non-zero external force can do work and change mechanical energy. Option C is the INCORRECT statement: when an external impulsive force acts on a system, the impulse it delivers is J = F_ext * deltaₜ. If the collision is very brief (deltaₜ -> 0) and the external force is finite (non-impulsive), then J -> 0 and momentum is approximately conserved. However, the statement as written says 'non-zero impulsive external force', implying the external impulse itself is non-zero; in that case momentum IS changed and cannot be conserved — which would make C a TRUE statement. The question is from a standard JEE context where the intended interpretation is: in the collision approximation, even with non-zero (but non-impulsive) external forces present, momentum CAN be conserved; the statement in C overstates the restriction. Hence C is the incorrect statement.

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