Match the following
`{: ( "Column I", " Column II"),(" (A) Example of conservative force ", "(p) Work done by all forces " ) ,("(B) Potential energy defined for only " , "(q) Force constant (spring constant)"), ("(C ) If two spring are stretched by same force, then ratio of their potential energy is in the inverse ratio of their " , "(r) Gravitational force"),("(D) Change in kinetic energy is equal ", "(s) Conservative force"):}`

Options

A. `A-q, B-p, C-s, D-r`
B. `A-r, B-q,C-p, D-s`
C. `A-r, B-s, C-q, D-p`
D. `A-q, B-r, C-s,D-p`

Explanation

To solve the matching question, we need to carefully analyze each item in Column I and match it with the correct item in Column II based on the definitions and properties of forces, potential energy, and kinetic energy.

### Step-by-Step Solution:

1. **Match (A) Example of conservative force:**
- A conservative force is defined as a force for which the work done is independent of the path taken and depends only on the initial and final positions.
- The gravitational force is a classic example of a conservative force.
- **Match:** (A) → (r) Gravitational force.

2. **Match (B) Potential energy defined for only:**
- Potential energy is defined only for conservative forces. Non-conservative forces, such as friction, do not have a potential energy associated with them.
- **Match:** (B) → (s) Conservative force.

3. **Match (C) If two springs are stretched by the same force, then the ratio of their potential energy is in the inverse ratio of their:**
- The potential energy stored in a spring is given by the formula \( PE = \frac{1}{2} k x^2 \), where \( k \) is the spring constant.
- If two springs are stretched by the same force, the potential energy will be inversely proportional to their spring constants.
- **Match:** (C) → (q) Force constant (spring constant).

4. **Match (D) Change in kinetic energy is equal:**
- According to the work-energy theorem, the change in kinetic energy of an object is equal to the net work done on it by all forces acting on it.
- **Match:** (D) → (p) Work done by all forces.

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