Conservation Of Linear Momentum

Drawing on NCERT Class 11, Chapter 5 (Laws of Motion), the principle of conservation of linear momentum states that in the absence of an external force the total momentum of a system remains constant. Before the explosion the object is at rest, so the total initial momentum is zero. The internal explosive forces are action-reaction pairs and cannot change the total momentum. Therefore the total momentum after the explosion must also be zero, meaning the two fragments carry equal and opposite momenta. For the 2 kg fragment, momentum magnitude is 2 × 9 = 18 kg·m/s. The 3 kg fragment must carry 18 kg·m/s in the opposite direction, so its speed is 18 / 3 = 6 m/s. Option 4 m/s wrongly divides the 2 kg fragment's speed scaled by mass ratio incorrectly. Option 9 m/s assumes equal speeds, ignoring the different masses. Option 13.5 m/s incorrectly multiplies rather than conserving momentum. A useful insight is that although total momentum stays zero, the total kinetic energy after the explosion is greater than before, the extra energy coming from the stored chemical or potential energy released in the blast. This shows that momentum conservation and energy conservation are independent ideas and must not be confused. Plausibility check: the lighter fragment moves faster (9 m/s) and the heavier fragment slower (6 m/s), which is exactly what equal-and-opposite momentum requires, confirming the answer.