UPSC NDA I 2023 General Ability Solved Paper

Concept:The force needed to keep the conveyor belt moving at constant speed equals the rate of change of momentum of the sand that lands on it.Explanation:Sand falls vertically onto the belt with a mass flow rate of $0.1\ \text{kg/s}$.The belt moves horizontally at a constant speed of $2\ \text{m/s}$.When sand lands, it immediately acquires the belt's horizontal speed.Thus, the horizontal momentum gained per second by the sand is:$\text{rate of change of momentum} = v \cdot \frac{dm}{dt}$= $2\ \text{m/s} \times 0.1\ \text{kg/s} = 0.2\ \text{kg m/s}^2$ (which is $0.2\ \text{N}$).To keep the belt moving at uniform speed, an external force must be applied to balance this momentum change.No net force is required to accelerate the belt itself because its velocity is constant.Therefore, the required external force is $0.2\ \text{N}$ in the direction of the belt's motion.Answer:$0.2\ \text{N}$ (Option B)