AIIMS 2018 Physics Variable Mass Systems MCQ Question

To find the speed of the system when the cart has 100 kg of sand, we can use the principle of conservation of momentum. Initially, the cart has a mass of 150 kg and is subjected to a constant horizontal force of 10 N, resulting in an acceleration of $a = \frac{F}{m} = \frac{10 \, \text{N}}{150 \, \text{kg}} = \frac{1}{15} \, \text{m/s}^2$. Over time, as 100 g/s of sand is added, the total mass becomes 250 kg (150 kg cart + 100 kg sand). The final speed $v$ can be calculated using the equation $v = u + at$, where $u$ is the initial speed (0 m/s) and $t$ is the time taken to accumulate 100 kg of sand at 100 g/s, which is 1000 seconds. Thus, the speed of the system is $v = 0 + \left(\frac{1}{15} \, \text{m/s}^2\right) \times 1000 \, \text{s} = 66.67 \, \text{m/s}$, but considering the options, we find that the effective speed is derived from the momentum conservation, leading to a final speed of 40 m/s when accounting for the mass increase and the force