Physics · System Of Particles And Rotational Motion · NEET
No. Internal forces always come in action-reaction pairs (Newton's third law). If particle 1 pushes particle 2 with force F, particle 2 pushes particle 1 with force -F. These add to zero, so all internal forces cancel out. That is why only the total EXTERNAL force can change the total momentum P. Individual particles can move in complicated paths, but P of the whole system stays fixed if external force is zero.
It is still zero. Before the explosion the bomb is at rest, so P = 0. The explosion is caused by internal forces only (no external push in the horizontal direction, ignoring gravity for the short blast). So the total momentum stays zero. The pieces fly out in different directions, but their momentum vectors add up (as vectors) to zero. The centre of mass stays exactly where the bomb was (or keeps moving as a projectile if gravity acts).
Momentum conservation only needs the total external force to be zero — it does not care about the type of force inside. Kinetic energy, on the other hand, can be stored or released by internal forces (chemical energy in an explosion, heat and sound in an inelastic collision). So P stays constant, but KE can increase (explosion) or decrease (inelastic collision). For NEET, always apply momentum conservation first; only use energy conservation if the collision is stated as elastic.
No. Since they start from rest, P = 0 and v_cm = 0 at the start. The attraction is an internal force, so total external force is zero and P stays zero. Therefore v_cm remains zero — the centre of mass never moves, even though both particles rush toward each other. This is exactly the NEET 2023 question: the answer is v_cm = zero.
Two particles A and B, initially at rest, move towards each other under their mutual attraction. When A's speed is v and B's speed is 3v, the speed of the centre of mass of the system is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
When the total external force acting on a system of particles is zero, the total linear momentum of the system (P = m1v1 + m2v2 + ...) stays constant in both magnitude and direction. Equivalently, the velocity of the centre of mass remains constant.
P = M v_cm, where M is the total mass of the system and v_cm is the velocity of the centre of mass. If the total external force is zero, then P = constant, so v_cm = constant.
Linear momentum is a vector. So conservation applies component-wise: if the external force is zero along a certain direction (say x), then P_x is conserved even if forces act in other directions. This is useful in 2D collision and explosion problems.
Recoil of a gun: the gun and bullet are at rest, so total momentum is zero. When fired, the bullet moves forward with momentum m×v and the gun recoils backward with equal and opposite momentum M×V, so m×v = M×V and total P stays zero. Rocket propulsion works the same way.
NEET often tests it as a one-line trick: 'system starts at rest, only internal forces act, find v_cm.' The answer is always zero. It also underlies collisions, explosions, recoil, and rocket questions, so mastering it saves time on many System of Particles and mechanics problems.
