Hello, I'm trying to figure out which of the following statements are TRUE.

Question

I suspect that 2, 6, 8 are true...and that there is one more that is true, but not sure which one?
Thanks!

It is impossible to have a collision between two objects in which the center-of-mass of the system is stationary the entire time.

If the magnitude of the momentum of one object is smaller after the collision than it is before the collision, the magnitude of the momentum of the other object must be larger after the collision than it is before the collision.

The vector sum of the momenta of the two objects before the collision equals the vector sum of the momenta of the two objects after the collision.

Momentum and kinetic energy are always conserved.

Momentum and kinetic energy are conserved only when the collision is elastic (when the elasticity equals 1).

The magnitude of the change in momentum for one object in the collision is equal to the magnitude of the change in momentum for the other object in the collision.

The motion of the center-of-mass is completely unaffected by any change in the elasticity of a collision.

Momentum is always conserved, but kinetic energy is conserved only when the collision is elastic.

If the center-of-mass of the system is moving in one direction before the collision it must move in the opposite direction after the collision.

Answer 1

It is impossible to have a collision between two objects in which the center-of-mass of the system is stationary the entire time.
1. false

If the magnitude of the momentum of one object is smaller after the collision than it is before the collision, the magnitude of the momentum of the other object must be larger after the collision than it is before the collision.
2. true

The vector sum of the momenta of the two objects before the collision equals the vector sum of the momenta of the two objects after the collision.
3. true

Momentum and kinetic energy are always conserved.
4. false

Momentum and kinetic energy are conserved only when the collision is elastic (when the elasticity equals 1).
5. true

The magnitude of the change in momentum for one object in the collision is equal to the magnitude of the change in momentum for the other object in the collision.
6. true

The motion of the center-of-mass is completely unaffected by any change in the elasticity of a collision.
7. true

Momentum is always conserved, but kinetic energy is conserved only when the collision is elastic.
8. true

If the center-of-mass of the system is moving in one direction before the collision it must move in the opposite direction after the collision.
9. false

Answer 2

ans above is incorrect, though I don't know what is wrong, just that I got it wrong

Answer 3

2 is false

Answer 4

It is impossible to have a collision between two objects in which the center-of-mass of the system is stationary the entire time.
False

If the magnitude of the momentum of one object is smaller after the collision than it is before the collision, the magnitude of the momentum of the other object must be larger after the collision than it is before the collision.
False

The vector sum of the momenta of the two objects before the collision equals the vector sum of the momenta of the two objects after the collision.
True

Momentum and kinetic energy are always conserved.
False

Momentum and kinetic energy are conserved only when the collision is elastic (when the elasticity equals 1).
True

The magnitude of the change in momentum for one object in the collision is equal to the magnitude of the change in momentum for the other object in the collision.
True

The motion of the center-of-mass is completely unaffected by any change in the elasticity of a collision.
True

Momentum is always conserved, but kinetic energy is conserved only when the collision is elastic.
True

If the center-of-mass of the system is moving in one direction before the collision it must move in the opposite direction after the collision.
False