Final answer:
Trolley B must have the greater mass than trolley A because after the inelastic collision, the system of the two trolleys moves at less than half of A's original speed, suggesting that the mass of trolley B significantly influenced the post-collision velocity.
Step-by-step explanation:
The question concerns a collision scenario where trolley A, moving towards the right, collides with stationary trolley B, and they stick together, moving off at less than half of A's original speed. To determine which trolley has the greater mass, we can apply the law of conservation of momentum. According to this law, the total momentum before the collision must equal the total momentum after the collision. Since trolley A's speed is reduced to less than half following the collision while sticking to trolley B, it implies that trolley B has the larger mass. If the masses were equal or if trolley A had a larger mass, the combined speed would have been closer to half of A's initial speed.
Therefore, the correct answer is B. Trolley B has the greater mass because the mutual speed of the trolleys after the collision is less than half of A's initial speed, indicating that the stationary trolley B had to have a significant enough mass to substantially decrease the system's speed upon sticking to trolley A.