Which of the following statements is/are true ?

Options

A. momentum is conserved in elastic collisions but not in inelastic collisions.
B. total energy is conserved in elastic collisions but momentum is not conserved in elastic collisions.
C. total kinetic energy is not conserved but momentum is conserved in inelastic collisions.
D. Kinetic energy and momentum are conserved in all typed of collisions.

Answer

To determine which of the statements regarding collisions are true, we need to analyze each statement based on the principles of momentum and energy conservation in elastic and inelastic collisions.

### Step-by-Step Solution:

1. **Understanding Momentum Conservation**:
- Momentum is conserved in a collision if there are no external forces acting on the system. This means that the total momentum before the collision is equal to the total momentum after the collision.

2. **Elastic vs. Inelastic Collisions**:
- In an **elastic collision**, both momentum and kinetic energy are conserved. The objects involved in the collision bounce off each other without any deformation or generation of heat.
- In an **inelastic collision**, momentum is conserved, but kinetic energy is not. Some kinetic energy is transformed into other forms of energy, such as heat or potential energy due to deformation.

3. **Evaluating the Statements**:
- **Statement 1**: "Momentum is conserved in elastic collision, not in an inelastic collision."
- This statement is **false** because momentum is conserved in both elastic and inelastic collisions.
- **Statement 2**: "Total energy is conserved in elastic collision but momentum is not conserved in elastic collision."
- This statement is **false** because both total energy and momentum are conserved in elastic collisions.
- **Statement 3**: "Total energy is conserved, not conserved but the momentum is conserved in elastic collision."
- This statement is **false** because in elastic collisions, both momentum and kinetic energy are conserved.
- **Statement 4**: "The kinetic energy and momentum are conserved in all types of collision."
- This statement is **false** because while momentum is conserved in all types of collisions, kinetic energy is only conserved in elastic collisions.

4. **Conclusion**:
- All the statements provided are false based on the principles of conservation of momentum and energy in collisions.

### Final Answer:
None of the statements are true.