Angle batween velocity and acceleration vectors in the following case
`{:("List-I", "List-II"),((A)"Vertically projected body",(e)90^(@)),((b) "For freely falling body",(f)"Changes from point to point"),((C)"For projectile",(g)"Zero"),((d)"In uniform circular motion",(h)180^(@)):}`

Options

A. a-h, b-g, c-f, d-e
B. a-f, b-g, c-h, d-e
C. a-e, b-f, c-h, d-g
D. a-g, b-h, c-e, d-f

Answer

To solve the problem of determining the angle between velocity and acceleration vectors for various motion scenarios, we will analyze each case step by step.

### Step-by-Step Solution:

1. **Vertically Projected Body (A)**:
- When a body is projected vertically upwards, its velocity vector is directed upwards.
- The acceleration due to gravity acts downwards.
- Therefore, the angle between the velocity vector (upwards) and the acceleration vector (downwards) is 180 degrees.
- **Match**: A → H (180°)

2. **Freely Falling Body (B)**:
- For a freely falling body, both the velocity and acceleration vectors are directed downwards.
- Since both vectors are in the same direction, the angle between them is 0 degrees.
- **Match**: B → G (0°)

3. **Projectile Motion (C)**:
- In projectile motion, the velocity vector changes in direction as the projectile moves along its path (it has both horizontal and vertical components).
- However, the acceleration due to gravity always acts downwards.
- As the projectile moves, the angle between the velocity vector and the acceleration vector changes from point to point.
- **Match**: C → F (changes from point to point)

4. **Uniform Circular Motion (D)**:
- In uniform circular motion, the velocity vector is always tangent to the circular path, while the acceleration vector (centripetal acceleration) points towards the center of the circle.
- The angle between the tangent (velocity) and the radius (acceleration) is 90 degrees.
- **Match**: D → E (90°)

### Final Matches:
- A → H (180°)
- B → G (0°)
- C → F (changes from point to point)
- D → E (90°)

### Conclusion:
The correct matches are:
- A with H
- B with G
- C with F
- D with E