AIIMS 2018 Physics Conservation of Momentum MCQ Question

To determine the velocity of the cart when all the sand has leaked out, we can apply the principle of conservation of momentum. The initial momentum of the system (cart plus sand) is equal to the final momentum when the sand has completely leaked out. The cart's mass is 2000 kg (1 metric ton) and the sand also has a mass of 1000 kg. As the sand leaks at a rate of 0.5 kg/s, it will take 2000 seconds for all the sand to exit. During this time, the cart will gain momentum, and using the equation $v = \frac{m_{sand} \cdot v_{sand}}{m_{cart}}$, we find that the velocity of the cart must be approximately 13.86 m/s to maintain momentum balance.

Options A, B, and C are incorrect as they do not satisfy the conservation of momentum principle for the given mass and leakage rate.