Match the following :
`{:(,"Column -I",,"Column -II"),((A),"Acceleration due to gravity",(p),"Kepler's law"),((B),"Law of periods",(q),"Vector quantity"),((C ),"Orbital speed",(r ),"Uniform near earth surface"),((D),"Gravitational potential",(s),"Is nearly zero at infinity"):}`

Answer

To solve the matching question, we need to pair the items in Column I with the correct items in Column II based on our understanding of gravitational concepts. Let's analyze each item step by step.

### Step-by-Step Solution:

1. **Acceleration due to gravity (A)**:
- The acceleration due to gravity (g) is a vector quantity that describes the acceleration experienced by an object due to the gravitational force of the Earth.
- Therefore, it matches with (q) "Vector quantity".
- **Match**: A → q

2. **Law of periods (B)**:
- Kepler's third law, also known as the law of periods, states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.
- Hence, it matches with (p) "Kepler's law".
- **Match**: B → p

3. **Orbital speed (C)**:
- The orbital speed of an object in a circular orbit is given by the formula \( v = \sqrt{\frac{GM}{r}} \).
- Near the Earth's surface, this speed is considered uniform because the values of G and M are constant for small heights above the surface.
- Therefore, it matches with (r) "Uniform near earth surface".
- **Match**: C → r

4. **Gravitational potential (D)**:
- The gravitational potential (V) at a distance r from a mass M is given by \( V = -\frac{GM}{r} \).
- As r approaches infinity, the gravitational potential approaches zero, indicating that it is nearly zero at infinity.
- Thus, it matches with (s) "Is nearly zero at infinity".
- **Match**: D → s

### Final Matches:
- A → q
- B → p
- C → r
- D → s