Which of the following statement is true for collisions-

Options

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

Answer

To determine which statement is true for collisions, we will analyze each statement step by step.

### Step 1: Understand the definitions of collisions
- **Elastic Collision**: In an elastic collision, both momentum and kinetic energy are conserved. There is no deformation or generation of heat.
- **Inelastic Collision**: In an inelastic collision, momentum is conserved, but kinetic energy is not conserved due to deformation and heat generation.

### Step 2: Analyze each statement

1. **Statement 1**: "Momentum is conserved in elastic collision, but not in elastic collision."
- **Analysis**: This statement is incorrect. Momentum is conserved in all types of collisions (elastic and inelastic) as long as there are no external forces acting on the system.

2. **Statement 2**: "Total kinetic energy is conserved in elastic collision, but momentum is not conserved."
- **Analysis**: This statement is incorrect. While it is true that total kinetic energy is conserved in elastic collisions, momentum is also conserved in all types of collisions, including elastic ones.

3. **Statement 3**: "Total kinetic energy is not conserved in elastic collision, but the momentum is conserved."
- **Analysis**: This statement is incorrect. Total kinetic energy is conserved in elastic collisions, while it is not conserved in inelastic collisions.

4. **Statement 4**: "Total kinetic energy and momentum both are conserved in all types of collision."
- **Analysis**: This statement is incorrect. Momentum is conserved in all types of collisions, but total kinetic energy is only conserved in elastic collisions.

### Conclusion
- The correct statement regarding collisions is that **momentum is conserved in all types of collisions**, and **total kinetic energy is conserved only in elastic collisions**. Therefore, the correct answer is that **total kinetic energy is conserved in elastic collisions, and momentum is conserved in all collisions**.

### Final Answer
The correct statement is: **Total kinetic energy is conserved in elastic collisions, and momentum is conserved in all types of collisions.**

---