AIIMS 2018 Physics Conservation of Momentum MCQ Question

To solve for the mass of the third part, we apply the principle of conservation of momentum. The momentum in the x-direction from the first part (1 kg at 12 m/s) is 12 kg·m/s, and the momentum in the y-direction from the second part (2 kg at 8 m/s) is 16 kg·m/s. The third part, moving at 4 m/s, must balance the total momentum in both directions, leading to the equation $m_3 \cdot 4 = \sqrt{12^2 + 16^2}$, which simplifies to $m_3 = 5$ kg. Options B (7 kg), C (17 kg), and D (3 kg) do not satisfy the momentum conservation equations, confirming that only option A is valid.