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Two carts A and B are identical in all respects. They roll down a hill and collide as shown in the figures at the right. Figure (i): Cart A starts from rest on a hill at a height h above the ground. It rolls down and collides head-on with cart B which is initially at rest on the ground. The two carts stick together. Figure (ii): Carts A and B are at rest on opposite hills at heights h/2 above the ground. They roll down, collide head-on with each other on the ground and stick together. 1. Which of the following statements are true about the two-cart system just before the carts collide in the two cases? Give all the statements that are true. If none are true, write N. The kinetic energy of the system is zero in case (ii). The kinetic energy of the system is greater in case (i) than in case (ii). The kinetic energy of the system is the same in both cases. The total momentum of the system is greater in case (ii) than in case (i). The total momentum of the system is the same in both cases.

2. Which of the following statements are true about the two-cart system just after the carts collide in the two cases? Give all the statements that are true. If none are true, write N.

1. The kinetic energy of the system is greater in case (ii) than in case (i)
2. The kinetic energy of the system is the same in both cases.
3. The momentum of the system is greater in case (ii) than in case (i).
4. The total momentum of the system is non-zero in case (i) while it is zero in case (ii).
5. The total momentum of the system is the same in both cases.

* Adapted from the ECS by Chandralekha Singh.

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